I count 12 threads per cm, not 13, and it looks smaller than 5 mm diameter to me. I'm nearly certain that it's a 10-32 screw, 7/8" long. The head is smaller than a typical pan head (probably came from something mass produced.) If the space for the head is small diameter and a pan head won't fit, a fillister head might.
And I disagree that M5x0.8 and 10-32 are interchangeable. Maybe in soft plastic where you can force a new set of threads, or with narrow nuts that only have a few threads, but generally, no.