A fraction p/q is in its lowest terms and its decimal expansion stops after exactly 5 places. Which of these could q be?

A fraction terminates only when q is built from 2s and 5s alone, and the number of decimal places is the LARGER of the two indices — because you multiply top and bottom by whichever prime is in short supply to reach a power of 10. Here $32=2^5$ gives exactly 5 places: 1/32 = 0.03125. The others miss: $40=2^3\times 5$ has larger index 3 (1/40 = 0.025), $250=2\times 5^3$ also has larger index 3 (1/250 = 0.004), and $64=2^6$ runs to 6 places (1/64 = 0.015625). Adding the indices instead of taking the larger is the usual slip — it would wrongly promote 40 to four places.