10-32 is VERY close to M5-0.80. The 32 is 32 threads/inch for a pitch of 1/32" or 0.7938mm. A 10-32 screw will screw into a deeply tapped hole over 10mm.

Now for more than you wanted to know, the "English" number system derivation is not known to me, but the size "N" can be converted to inches by 13*N+0.060. Thus a #10 screw is 0.190". The M5 is 0.197".

Many think that a #10 is 3/16"; close, but not exact. What I've been told by 2 different fastener salesmen many years ago is that the product tolerances are such that a modern (we're talking 1970s here, so better yet today) threading machines can make a thread that will meet both the 3/16"(0.1875") and the #10 (0.190") dimension standards, so one screw is sold for both. I'm not sure ...