Erections are rather revealing to ones health and, unfortunately, one's age as well. Somatically speaking diabetes is the most common cause of erectile failure, but that occurs at the outset, not after 5 minutes. Hypertension, atherosclerosis (particularly in midsized vessels - a unique pattern of uncertain etiology) and some forms of liver disease or prostatism of various types can be the culprit.
But then, there's the hormone thing. By 55, about 35% of men are no really no longer interested in sex - mostly because (deep down) they just don't feel like it. By 60 that's about 45%; by 65 it's 65% and by 70 it's about 75 - 80%. In some men, the "desire" is there mentally, but the real visceral (hormone-driven) urge just isn't. An erection that occurs (often no problem at the start) but disappears quickly is the symptom of this. Other symptoms are presence of pre-ejaculation fluid well before the erection, and delayed ejaculation well after the orgasm is over.
Get your T level tested. They can be remarkably low by the late 50's. Although I have some reservations regarding the methods used for T-replacement such could possibly bring your body up to par with your head, but up to now this is not often the case, and, there are side effects with overdosing.
You're in your late 50's and you feel like you're 30, but that is no guarantee your testicles "feel" the same.