Let numbers be x and y with x - y = 5 and xy = 336. Then (x + y)² = (x - y)² + 4xy = 25 + 1344 = 1369, so x + y = √1369 = 37. Options A (21), B (51), and C (28) don't satisfy this relationship. This uses the identity (x+y)² = (x-y)² + 4xy.
Let the two numbers be x and x+5. Their product is x(x+5) = 336, which solves to x = 16 and x+5 = 21. Adding these gives a sum of 37, matching the correct option through straightforward quadratic solving.