For 5/16" BSW bolts and setscrews, the standard head dimensions are as follows;
Precision hexagon bolts and setscrews to BS1083:1951 -
Width across flats 0.525 max 0.518 min.
Head thickness 0.22 max 0.21 min
Bright hexagon bolts and setscrews, old standard BS190:1924 -
Width across flats 0.600 max 0.595 min
Head thickness 0.27 max 0.26 min
Black bolts BS916:1953
Width across flats 0.525 max 0.515 min
Head thickness 0.218 max 0.198 min
Black bolts, old standard BS28
Width across flats 0.600 max 0.580 min
Head thickness 0.29 max 0.27 min
All dimensions are in inches. Info taken from Machinery's Screw Thread Book, 19th edition, 1965.
If the dimensions don't accord with any of the above, they're specials.