How powerful is your flash unit?
A Vivitar 285HV on full manual (GN 120) using 400 speed film at 7.5 feet requires f/32.
A Sunpak 622 Super on full manual (GN 200) using 400 speed film at 7.5 feet requires f/53.
A Meggaflash PF200 type A-19 flashbulb (GN 420 at 1/30 sec or less) using 400 speed film at 7.5 feet requires f/112.
A Meggaflash PF300 type A-23 flashbulb (GN 550 at 1/30 sec or less) using 400 speed film at 7.5 feet requires f/147.
That last PF300 flashbulb option would seem to match up closely with Jim's recommendation for a 0.15mm pinhole size, since 21mm divided by 147 is 0.143mm. Unfortunately those PF300 bulbs sell at Cress Photo by the case lot (48 bulbs) for USD$630.00 per case, or $13.13 per bulb. Apparently scientists, railroad photographers and spelunkers are the major users of these still-in-production modern flashbulbs.
The problem here is that for a pinhole camera 5-10 feet away is a lot (unless you have access to some big-boy studio flash units)...