Did they say 5 miles, instead of 5 km? Effective radar range depends on lots of factors, including speed, amount of superstructure, course, sea state. bobbing of the target, height over horizon etcetera. Sometimes atmospheric conditions cand help, or hinder range too. The power output of the radar also helps increase range, as the stronger the outgoing signal, the stronger the echo.
Paraphrased from U.S. Submarines through 1945. An illustrated Design History.:
The first SJ radar attack was conducted by the USS Haddock on 22nd August 1942. She had hit a transport, which had fled the area and the Haddock surfaced and pursued. It was a moonless night, so she had to rely on her SJ Radar. She detected the target at 13,000 yards (approx 12km or 6.5 nautical miles), tracked it, closed and sank it at 1,300 yards.
SJ was upgraded to SJ-a starting in the summer of 1942, this involved adding a PPI scope and and a variable trainiing mechanism, then a year later radar was upgraded to SJ-1 in the summer of 1943. This had 50% more power and consequently more range. Quoted ranges for the SJ-1 is 12 nm for a battleship and 5nm for a submarine (small target).
Radar changed the way attacks were made as it allowed attacks at night with no light with conditions favourable to the submarine. Attacking on the surface gives much more flexibility in the way you conduct your attack. In 1942 when few submarines had radar, 30% of attacks were conducted on the surface at night (preferably attacking from a direction that put the moon in a favourable position to light the targets, but not the submarine). In 1944, surface attacks at night accounted for 57% of all attacks and at the end of the war many COs passed up daylight opportunities to take advantage of better conditions at night.
EDIT: I remember reading a war patrol, where it said they picked up a BB at a range of 36,000 yards and that this was noted as exceptional performance. I think it was one of the USS Pampanito's late war patrols.
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