Unlike the levers themselves these clamps rarely ever had sliding problems.

I suggest you remove the clamp, slide it out of the way, and clean the area completely to remove any possible oil film. Then remove the screw and work nut up and down the threads using some oil to clean them up and reduce any thread friction.

Then put it all back together and tighten to what you feel approaches the torque limit for a 5mm screw. (roughly 3nm max.)

If you don't feel it'll hold, go to your friendly auto mechanic and beg a tiny bit of lapping compound. Slide the clamp out of the way, apply some compound to the frame where you'll be putting the clamp, then with it fully loose put it where you want it and tighten. When the band is tight the grit in the compound will bite into both the clamp and frame, locking them together.

WARNING - when you use lapping compound this way, you cannot slide a slightly loose part to reposition it. You always have to loosen completely, move, then thighten.