Here are my experiences which could be instructive for you. I'm 10yrs older than you and not as fast but it's close enough. I'm 5'9" and I did pay for professional coaching at all phases of my running "career" sited below.
38yrs old: Functioning alcoholic. 185lbs (27 BMI) 70 drinks per week/20-30 mpw/ate anything. HM 1:30:09
41yrs old: Sober. 170lbs (25 BMI)/ 25-35 mpw/ ate anything HM 1:26:xx (I don't remember)
42yrs old: Sober. 155lbs (23 BMI)/30-40 mpw/ ate primarily plant based and thoughtfully HM 1:23:37
N.B. HM at 38yrs was NYC HM (the old course) and HM's at 41/42 were Philly so a little faster probably less than 30s though. All were run in March/ comparable weather.
You will see improvement not just from being lighter but if you do clean up your lifestyle you will be able to train harder, sleep better, recover better and def in my case be happier. Good luck to you.