SOLUTION: Find a counterexample to the statement “The square of a number added to the sum of the number and five is a prime number”

By trial and error.

Try 1:
"The square of 1, which is 1, added to the sum of 1 and five, which is 6,
is the prime number 7."

Nope, that's an example, not a counterexample.

Try 1:
"The square of 2, which is 4, added to the sum of 2 and five, which is 7,
is the prime number 11."

Nope, that's an example, not a counterexample. 

Try 3:
"The square of 3, which is 9, added to the sum of 3 and five, which is 8,
is the prime number 17."

Nope, that's an example, not a counterexample.

Try 4:
"The square of 4, which is 16, added to the sum of 4 and five, which is 9,
is 25, which IS NOT a prime number, since 25 is divisible by 5."

Yes, finally, a counterexample!

Edwin