To make the inequality \( N + 1 > 4 \) true, we can rearrange it to find the values of \( N \) that satisfy the condition:
\[ N > 4 - 1 \] \[ N > 3 \]
From the given set of numbers \( {1, 2, 3, 4, 5} \), the values of \( N \) that satisfy the inequality \( N > 3 \) are:
- \( 4 \)
- \( 5 \)
So, \( N \) can be either \( 4 \) or \( 5 \) to make the inequality \( N + 1 > 4 \) true.