I'm no expert but I would have thought a small would likely be better.
It's not possible to be sure anyway from just a height and inseam measurement. Have you had a bike fit?

P.S. I presume 31.4961" inseam is 800mm? ;) I found it difficult to be sure of mine to the nearest 5mm, nevermind 0.0001" precision!

Im 5'8 inseam 31. I ride a small plasma 5. Fits perfectly.

If it is your friend is it possible to test ride first? I think the Medium could potentially work, I have a few teammates about your size on the medium, but you may find that the small might be slightly better.

The Medium may be a bit too big. Hard to say - depends on your physiology. That's a lot of bike to buy without finding a fitter who'll do a fit on a fit bike. With a good fit and fit coordinates, figuring out which size would be best is an easy math problem.

Eyeballing you at 5'8, I'd probably put you on a Small.

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Trent Nix
Owned and operated Tri Shop
F.I.S.T. Advanced Certified Fitter | Retul Master Certified Fitter (back when those were things)

Just a tiny bit bigger then you and the M was to big for me.
Had to cut seat post but couldn't get front end low enough even with after market straight stem.

Just for some more confusion:

I'm 5'11.75" with a 32" inseam. I got a bike fit...they put me on a Plasma in Large. So...yeah....

You should be fine for a Medium I'd guess. It'll be on the big side, but I'm guessing it'd be more comfortable and work. Maybe not as aggressive, but doable.