NotThamesWater-
How much of your training involves running faster than 5min / km?
I've done a 6k run at 4:57/km (https://www.strava.com/activities/250275276) that had a 5k section that was done in 24:41, so I know it's possible right now. But it's easier to happen upon a fast run because I'm feeling good rather than setting out to do a 5k at a specific pace and blowing up part way round. Also depends on the parkrun conditions (how busy, how boggy the Common/Heath is, etc).
The simplest way it'll happen is that I continue to lose weight. I'm 84.5kg at the mo, and the VDOT/fellrnr guides say that getting down to 76kg (which gets my BMI under 25) means I should be aiming for a 22:35 5k. (It's safe to say I could drop those 8kg, and a bit more, without worrying about losing any muscle mass.) Once I do get down to a more sensible weight then the track/interval sessions will begin.
Last time I was 76kg was in 2009 when I did London-Edinburgh-London on the bike. Apathy and fatherhood after that helped me pile on the pounds.
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Greenbank
Wed: Rest (well, gentle swim with daughter and 2 or 3 miles of walking)
Thu: 12km run in to work, 8 hours rest slumped at desk, an hour of 5-a-side
Fri: 4k swim
Sat: 5k parkrun (hoping the supercompensation will kick in here, want a sub 25)