Is it permissible for a man in his sixties to masturbate to relieve back pain, especially if he leads people in prayer and his wife refrains from intercourse due to her own pains, and he is unable to marry another?

Masturbation is not permissible; it is a forbidden habit. If the wife is in pain during intercourse due to an illness, treatment must be sought. If your wife cannot relieve you and you are unable to marry another, then masturbation by the wife's hand or any part of her body is permissible.