Divisiblity Question

Find all positive integers n that satisfies:
n+1 \mid n^2+3n+5

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n+1 | n^2+3n+5-n(n+1)
n+1 | n^2+3n+5-n^2-n
n+1 | 2n+5
n+1 | 2n+5-2(n+1)
n+1 | 2n+5-2n-2
n+1 | 3

This means that n+1 has to be 3, and thus n = 2

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