How do I solve this problem?

4. Show that there is a natural number n so that n2 + 5 is a prime but for every natural number m smaller than n, the number m2 + 5 factors in a product of two numbers smaller than m2 + 5. Hint: This problem is motivated by the easily discernible fact that 722 + 5 = 5189. Wouldn't you like to solve this problem by using the Well Ordering Principle