number theory - proof - infinite pair integers $a$ and $b$ such that $a + b = 100$ and $gcd(a, b) = 5$

Prove that there are an infinite pair integers $a$ and $b$ such that $a + b = 100$ and $\gcd(a, b) = 5$.

I don't know how to proceed with this. Especially, proving that they are infinite. There was another problem when the GCD was 3 and I had to prove there existed no such combination, which I did with ease.

I have tried but have made no progress. Any help would be appreciated.

Answer

Thanks to Wojowu, I am able to present my proof. If you find any error or flaws please comment.

Proof:

$\forall k \in \mathbb{Z}^+ \gcd(100k+5, -(100k - 95)) = 5$

As, $\gcd(100k + 5, 100k - 95) = \gcd(100k + 5, 100k - 95 - (100k + 5)) = \gcd(5(20k+1), 5(20))$ which is equal to $5$ as $20k +1$ is relatively prime to $20$. Thus there are infinitely many pairs of integers that satisfy the given criteria.