Factoring a special RSA modulus from ASIS CTF 2021 Quals

LagLeg is a crypto challenge in ASIS CTF Quals 2021. We are asked to factor a given modulus $n$ such that $n = (r^5 + s)(r + s)$. Hereby $r$ and $s$ are respectively 256 and 64 bits long. I think my approach used is very unique - and definitely worth mentioning. It does not mean that it is a good approach, however. I will record the exact steps I solved the challenge. However, I will update the bounds and prove the whole thing so that it looked more rigorous. The full code will be attached at the end of the blog post, too.