The type 53-65 torpedo had the same range as ASROC right ?
It did, but that wasn't enough because ASROC and other ASW missiles have to add the range of their torpedoes to them. With this, the range of a 1960's ASROC+Mark 46 is 19+11, or 30 km. However,
this source and
this one state the range was only 10,000 yards (9.1 km), and
this source states the maximum range of the Mod 4 to be 16 km. With a 9.1 km range the maximum torpedo+ASROC range would be about 20.1 km, and with a 16 km range it would be 27 km. A 1993 VL-ASROC with a Mark 50 would have 22+15=37 km of range.
As such, the 53-57, 53-61, and 53-65 were not sufficient to fully outrange ASROC, unless the 9.1 km range is accurate, in which case the new models from 1969 could do so (they had a 22 km range). This is a consequence of inferior Soviet torpedo technology. The Mark 48 torpedo entering service 3 years later had over double the range with almost the same size warhead and less overall weight. To gain the usual ASuW performance expected from a submarine-launched torpedo, the Soviets had to increase the size to the 650 mm 65-76 (from 1976). This torpedo finally had the 50 km range comparable to a Mark 48 (though at much heavier weight), and enough to outrange ASROC like the Mark 48 did.
The 65-76 as such would be the main effective ASuW torpedo of the Soviet submarine force, and the one that fulfills the rule of submarine weapons outranging ASW weapons (even against the modern VL-ASROC with a Mark 50).
In short historical ranges of ASW and submarine weapons (marked with an S but the date) are:
unguided submarine torpedo range: depends, but HMS Barham's sinking at 375 meters was considered "close range" so max. effective range is likely around 750 m.
1910 (S): 750 m, unguided torpedo
1916: 0 m, depth charge
1917: 40 m, depth charge projector (Thornycroft)
1917: 73 m, depth charge projector (Y gun)
1917: 275 m, 7.5" (190 mm) ASW Howitzer Mark I (1,920 meter range was possible but with a 100 lb (45 kg) shell that was considered too small)
1918: 550 m, 11" (280 mm) ASW Howitzer
1940 (S): 1500 m, ungided torpedo with Torpedo Data Computer
1942: 183 m, Hedgehog
1943 (S): 3,650 m, Mark 18
1943 (S): 4,570 m, Mark 28 "Cutie"
1943: 250 m, Squid
1951: 695 m, Weapon Alpha
1955: 910 m, Limbo
1957 (S): 9,140 m, Mark 37 (range is 21,490 m at slower speeds)
1960: 24,500 m, ASROC+Mark 44 (19+5.5 km)
1966: 30,000 m, ASROC+Mark 46 (19+11 km)
1972 (S): 32,000 m, Mark 48 Mod 0 (estimated at max performance, range is closer to 50,000 m at slower speeds)
1976 (S): 50,000 m, 65-76
1987 (S): 50,000 m, Mark 48 ADCAP (estimated)
1991 (S): 100,000 m, 65-76A
1993: 37,000 m, VL-ASROC+Mark 50 (22+15 km)
2012 (S): 140,000 m, DM2A4 ER