I have a RaceFace Ride crank with Shimano BB70 cups. There is a 2.5mm spacer on each side between the frame and cups. I have tightened the crank up to the max, yet I can still move the crank side to side a few mm's. What basic tomfoolery have I enacted?

Have you tighten the cups to the frame ? if not you will get movement as you have notice . Other than that it could be wore seals and/or bearings .

And you have ID'd the cause of the issue yourself. You need 2 x 2.5mm spacers on the drive side & 1 on the NDS (you should have been supplied with either 3 x 2.5mm or 2 x 2.5mm, 1 x 1.8mm & 1 x 0.7mm) https://techdocs.shimano.com/media/te...9830674840.pdf

Well, thank you!

I'd found a little spacer table for various crank/cup combos on the park tools blog, but it only listed 1 max either side. (I got the bike whole off a friend, so I shall be chasing him for spacing.)