Its an interesting departure point - partly because much of the early Tudor period was in fact a continuation of Yorkist policy.
You have senior peers closely related to the throne - Anthony 2nd Earl Rivers, Edward Duke of Buckingham and Richard Duke of Gloucester. You also have the children of George Duke of Clarence - The Earl of Warwick and Lady Margaret growing to adulthood and the Queen's two children by her first marriage Thomas Marquess of Dorset and Richard Grey.
Richard's resentment of the Woodville's before his brother's death is just not in evidence (despite the views of many Ricardians) in this scenario you have an adult succession so no arguement over Protectorship or Regency. Buckingham on the other hand does resent the Yorkist regime he is married to the Queen's sister, but resents the fact that much of the political influence that should have been his has been kept from him. Anthony 2nd Earl Rivers has been the guardian of the young Prince of Wales in Ludlow since his household was established there and unlike many of the Queen's other relations has remained close to both her and Edward IV.
You also have a young King with powerful allies - Edward IV's plans for his numerous daughter's were ambitious - most had failed over his greed over the financial settlements and doweries for them but give him another seven years on the throne and its highly likely he would have had more success. More importantly to the future of Europe was that in 1480 Edward Prince of Wales was betrothed to the then 4 year old Anne of Brittany a marriage that could have taken place as early as 1490 - the deal would have guaranteed Brittany's independence - Anne's second son was to inherit Brittany under the terms of the Treaty whilst the eldest inherited England.
Here's a few suggestions of what might have happened in 1483 - Edward IV recovers from a strong illness early in the year - meanwhile in Europe - Maximillian of Austria, whose wife Mary of Burgundy died a year before, is forced to sign a treaty over the Burgundian possessions with the dying Louis XI of France - his daughter Margaret of Austria is despatched to the French court and betrothed to the new King of France Charles VII.
A resentful Maximillian under the advice of his wife's stepmother Margaret of York - approaches Edward IV (still bitter over his daughter Elizabeth being jilted by Charles VII) with an offer - confirmation of the betrothal of Anne of York to his young son Philip the Fair, Duke of Burgundy meanwhile Maximillian himself offers to marry Elizabeth of York immediately. In Brittany the treaty of marriage between Anne of Brittany and Edward Prince of Wales still looks the best deal to retain some independence for the Duchy, despite increasing pressure from France under the regency of Anne of France - Duke Francis in these circumstances is less likely to have been forced into the Treaty of Verger and its also likely that his daughter Anne of Brittany would have been sent to England by the time she was ten or eleven to ensure she was safe from French control.
By 1488 the situation has changed and France is now encircled by enemies - Anne of France faced with revolts invades Brittany determined to force the Bretons to repudiate the English betrothal - Edward IV determined to prevent that happening despatches an English Army to support the forces of Francis II of Brittany under the command of Richard Duke of Gloucester and his brother in law Anthony Lord Rivers. The larger English/Breton Army defeats the French at the Battle of Saint-Aubin-du-Cormier - shortly afterwards the French agree to the Treaty of Saint Malo fearing that if the war continues Edward's other ally Maximillian of Austria might join the fray - the French are forced to confirm Breton independence, to resume payments of their large pension to Edward IV in return Edward is forced to guarantee that Brittany wouldn't be absorbed into the English Throne. A few months later Duke Francis II dies - Anne is acknowledged as Duchess of Brittany at 11 years old.
The same year Edward IV's daughter Anne, is despatched to the care of Aunt Margaret Dowager Duchess of Burgundy ahead of plans for her marriage to Philip Duke of Burgundy the following year.
Also that year James III of Scotland is killed and his 15 year old son James is proclaimed James IV - despite rebellions James IV looks secure and Edward makes a formal offer reviving his proposals of marriage between his daughter Cecily - James realising the advantages of a peace deal - Signs the Treaty of Perpetual Peace with Edward IV in 1489 and marries the Princess Cecily.
In 1489 after 6 years of protracted negotiations, Edward IV, finally concludes details of the negotiations with Ferdinand and Isabella over the marriage of his daughter Catherine to Juan Prince of the Asturias - the young princess is despatched to the Spanish court and the care of her future mother in law Queen Isabella.
So by the accession of Edward V in say 1490 - the young King is also Duke of Brittany through his wife Anne (who he formally marries that year), his brother in laws are; the Duke of Burgundy, the King of Scots, the heir to the thrones of Aragon and Castille and the Archduke of Austria and future Holy Roman Emperor.
However at home he faces two Uncles with large apanages - the Duke of Buckingham and the Duke of Gloucester. And his unmarried 17 year old brother has also a large landed estate.
Potential problem - The Duke of Gloucester's only son had died in 1484 and his wife shortly thereafter - he has not so far remarried (much of his lands belonged to his wife's family and with her childless death - her relatives are clamouring for their rights to them to be restored - his wife's sister is Isabella dowager duchess of Clarence is just one person angling that all those lands should revert to her and thence to her son the teenaged Earl of Warwick) - a dispute between the King and Gloucester if he remarries and has a child over the Neville lands (settled by Edward IV over a decade earlier) could happen.
Buckingham - still a relatively young man and a rich one - deprived of influence that should rightly have been his he may be ripe for rebellion if his nephew by marriage doesn't grant him some authority particularly in Wales.
The Queen Mother - close to both her sons but perhaps more so to her younger son who unlike his brother remained at his parents court. However in OTL she died in 1492 in her mid fifties and its more than likely her life span would be similar in this TL.
Henry Tudor Earl of Richmond - the last real Lancastrian claimant however distant - was exiled in Brittany until Edward IV's deal with Francis II - then fled to France where Charles VII occassionaly promises him an army. However he is not regarded as a serious threat by anyone but his wealthy mother who wants him home and able to inherit her wealth.
The Marquess of Dorset - half brother to the King and a leading member of Edward IV's council - a bit of a rake but popular with the late King. A key figure in the South West and potentially could over reach himself. (along with his brother Richard Grey)
It is such a major change that it would cause serious ripples - an independent Brittany lasting longer a continual cause of potential war with France, no Spanish-Hapsburg union, the potential for Maximillian 1 to divide his inheritance between his son the Duke of Burgundy and his children by Elizabeth of York,an independent Dukedom in Burgundy that might in time have developed into an early Kingdom of the Netherlands with a ruling Hapsburg-Plantagenet dynasty who might have been attracted like so many of their subjects to the new learning and the new religion. As to religion - there's no guarantee that Edward V's son or grandson might not have been attracted to the wave of protestantism that spread across Northern Europe.
Betrothals of the House of York to 1483.
Elizabeth of York (b1466) - her betrothal to Charles VII of France was broken in 1482/3
Cecily of York - (b1469) betrothed to the future James IV (but broken when relations between Edward IV and James III fell apart)
Anne of York - (b1475) had been betrothed to Philip the Fair son of Mary of Burgundy and Maximillian of Austira in 1479 (the betrothal wasn't repudiated until after Edward's death in 1483)
Catherine of York - (b1479) within a month of her birth she was formally betrothed to Juan of Aragon (eldest son of Ferdinand and Isabella born 1478). Negotiations were ongoing in 1483.
Bridget of York - was only born in 1480 - and appears to have been dedicated by her parents to God very early (she entered Dartford Priory as early as 1487).
Richard Duke of York and Norfolk - born 1473 (his child bride Anne Mowbray died in 1481, but under the terms of a 1483 Parliamentary act Richard was to retain his wife's vast estates)