All we need to do is to find a common denominator for each of the fractions. It's quite easy in this case because each denominator is an iteration of 16, so so LCD is 64:
5/16 = 20/64
13/64 stays the same
9/32 = 18/64
And the hole's size: 3/16 = 12/64
12/64 < 13/64 < 18/64 < 20/64
So the smallest measurment but still larger than 3/16 (12/64) is 13/64 inch.