5/32" (.156 in) is not a standard screw size in any system that I know of. However, it is very close to a metric M4 size (.157 in), and just a bit smaller than a #8 (.164 in).
The thread pitch is important— a #8 machine screw will likely have 32 threads per inch (thread pitch = .031 in = 0.79 mm), while a M4 machine screw will probably have a thread pitch of 0.70 mm = .028 in (~36.3 threads/inch). While these numbers don't look like much difference, you will not be able to thread a machine screw very far into a nut or thread of a different thread system before it locks up.
If you really don't know whether it's inch or metric, then find a nut of a known size (#8 or M4) and see if it threads in easily. Now you know...
Sam B
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