A composite numer is one that has factors other than that number itself and 1.
Recall the multiplication theorems of odd and even numbers.
The product of three odds cannot be even.
We also know the adding theorems of whole numbers which says:
The sum of an odd and an even number will always be even.
Since even numbers are divisible by 2, we can confirm that 5×7×13+7 is not prime.
Therefore, 5×7×13+7 is a composite number.
5×7×13+7 = 462.
462 is an even number, it is divisible by 3, and so many other numbers.
It is clearly not prime.