Is the assumption that the five daily prayers expiate sins, based on the saying of the Prophet, peace and blessings be upon him: "Allah thereby erases sins," correct?

The assumption that prayer has no effect on someone who commits sins is incorrect. Prayer, if performed with its full rights and devotion, restrains from indecency and evil. Prayer does not increase one's distance from Allah; rather, it brings one closer to Him, even if they are a transgressor. One who prays while persisting in sins is deficient in their prayer and has not performed it in the prescribed manner. Prayer expiates minor sins, but major sins require a specific repentance, and persistence in minor sins transforms them into major ones.