**Solution: **

By the definition of a composite number, we know that if a number is composite, then it means it has factors other than 1 and itself. Therefore, for the given expression;

**7 × 11 × 13 + 13 **

Taking 13 as a common factor, we get,

= 13(7 × 11 × 1 + 1)

= 13(77 + 1)

= 13 × 78

= 13 × 3 × 2 × 13

Hence, 7 × 11 × 13 + 13 is a composite number.

Now let’s take the other number.

**7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 **

Taking 5 as a common factor, we get,

= 5(7 × 6 × 4 × 3 × 2 × 1 + 1)

= 5(1008 + 1)

= 5 × 1009

Hence, 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 is a composite number.