shaheed has the AR (4:53.01/4:50.95i) for 60-64 year olds, turnbull has the WR for 65 (4:56.4), but neither of these really answer the oldest to break 5 question, nor the oldest to break 5 for the first time (i doubt that's been tracked). not sure if a list exists for single year age group records in the mile. there is an unratified record for american dan king at 60yo (4:49) also.
as a 54yo (same age as the OP) i can confirm: breaking 5 is tough. you won't do it on just luck or talent. like P! (who are you? i thought i possibly had the longest current streak once steve spence's ended, but i stand corrected), i have a 41 year streak of sub-5s, and at least up until 50 it was pretty easy for me if i was healthy since i still compete regularly, and i'm still within a minute of my lifetime PR (i also ran the 1500m equivalent of 4:13/4:14 at ages 44/45). i ran a 4:52 a month ago to continue my streak, a month after turning 54, and i needed that month to gain fitness after being injured all summer. i'm pretty haphazard about my training so can't offer much advice, but i regularly run 50-70 miles per week when healthy with one night a week on the track and one semi-regular tempo-ish workout, so i put in a fair amount of work.
hoping i can make it to 60 running sub-5--a few years ago i would have thought that was an easy to achieve goal, but now i realize i'll have to be pretty deliberate and precise about my training to keep it going that long.
good luck with it--it's fun, or at least has been for me, but it ain't getting any easier...
carpe crepusculum,
cush