No. No chance whatsoever.
A lot of hard-training, pretty decent club runners in England couldn't break 15:00 when they were young.
Martin Rees who is a phenomenon, was 15:55 at 59, so you are talking about the best part of 20 seconds per mile faster.
We are looking at 4:50 per mile, and there are very few near 60 year olds who can run one mile at that pace.
Even if the genetics/cardio vascular ability is there, it's doubtful whether a 57+ body will withstand the training.
I've improved from 30 to 60 in age graded terms, and I've still lost at least 3 minutes. It's going to take Bekele, Farah like talent, and then keeping training for another 25 years without getting injured.