You have to look at it logical, If you want to break a 5K PR.
Where are you having the problem? If it's speed then I would work on your mile time. You'll need to get it down. Start with a 5:30 miles several times a week. Doesn't have to be an interval or on a track, just on days when you are fresh and warmed up.
If you have problems with the endurance, then put in a few more miles, which will also help you with weight.
I personally don't think it has anything to do with age.
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