We can factor the given expression as follows: \(p + p^2 = p(p+1)\)

So the given information is telling us that 5 is a factor of \(p(p+1)\)

This means 5 could be a factor of p, or 5 could be a factor of p+1

Let's examine each possible case:

case i: 5 is a factor of p
Another way to say this is: p is a multiple of 5
If p is a multiple of 5, then we will get a remainder of 0 when we divide p by 5

case ii: 5 is a factor of p+1
Another way to say this is: p+1 is a multiple of 5
So, some possible values of p+1 are: 5, 10, 15, 20, ....

If p + 1 = 5, then p = 4. When we divide 4 by 5, the remainder is 4
If p + 1 = 10, then p = 9. When we divide 9 by 5, the remainder is 4
If p + 1 = 15, then p = 14. When we divide 14 by 5, the remainder is 4

Answer: A, E