Very interesting thread, at least for us old farts. My 2 cents on the original question (though I agree with many of the above posts). For the record, I'm 44 and my best times in the last two years are 4:31.9 for the mile and 2:36 for the marathon, both at altitude in Montana.
I think that a masters runner needs the same basic training elements as a younger runner, if your goal is getting under 16 for the 5k.
Sub 16 or 5:08 per mile for a 5k will require getting to the point where a workout of 4 x mile around 5 flat with 400 jog recovery is do-able. In my experience, that pretty much requires doing one tempo and one interval workout a week. I find that nothing but intervals gets me to the point where 5 minute pace doesn't feel brutal right from the get-go. Tempo runs are important for me, but tempos alone do not get me ready mentally for the hammering, and do not get me ready to run relaxed at high pace.
I mostly train for trail races... for these, I think that interval workouts with total volume of 4-6 miles, tempo runs of 5-8 miles, and long runs of 1:30 to 2:00 are the basic ingredients of a training program that has worked out for thousands of people over many decades. If you're running well once a week in these three elements, you're going to race well.