The least number which when divided by 2, 7, 5 and 10 leaves zero remainder in each case and when divided by 13 leaves a remainder of 5 is:

70

Since we are looking for the number that leaves 0 as remainder with 2, 7, 5 and 10, we are actually looking for the LCM.

LCM of 2, 7, 5 and 10  =2 × 5 × 7 × 10  = 70

\(\frac{70}{13}\) = 5 remainder

So, the answer is 70