Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers?

By definition,

A composite number is a positive integer that has a factor other than 1 and itself. Now considering your numbers,

7×11×13 + 13 may be written as, i.e. 13 * (78). So other than 1 and the number itself, 13 and 78 are also the factors of the number. Further, 78 = 39 x 2. So, 39 and 2 are also its factors. So this number is definitely not prime. Hence its composite number.

Similarly, 7×6×5×4×3×2×1 + 5 can be written as , i.e. 5 * (1009). So, other than the number and 1, it have 5 and 1009 as its factors too. So it is also a composite number.