Thatd be the 5mm turned into inches is ~.2in, to feet thats .016ft for the bb's cross section. .016 divided by the 500f/s gives you the amount of seconds that the BB takes to go by a point (the sensor), then multiply that by 1000 to get the number of milliseconds that it takes to pass by.
5 mm at the speed of sound 340m/s ==> 0.005/340 ~ 14.7 microseconds
5 mm at 500 feet/sec 150 feet = 150 meter ==> 0.005/152.4 ==> 32.8 microseconds = 0.033 msec. (Your math is OK)
A pulse of 32.8 micros can be measured by an Arduino, the precision/stepsize using micros() is 4 micros() . If you use a hardware timer you can get more precise results.
See - Arduino Forum - for some detailed discussion.