Even Integer Plus 5 is Odd/Proof by Contradiction

Direct Proof
Let $x$ be an even integer.

Then by definition:
 * $x = 2 n$

for some integer $n$.

$y = x + 5 = 2 m$ for some integer $m$.

Then:

Hence $x$ is odd.

But this contradicts our premise that $x$ is even.

Hence the result by Proof by Contradiction.