Erdős Probelm 608

### What is the conjecture

https://www.erdosproblems.com/608

Let $G$ be a graph with $n$ vertices and at least $\lfloor n^2/4\rfloor +1$ edges. Are there at least $2n^2/9$ edges of $G$ which are contained in a $C_5$?

Status: falsifiable

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start by reviewing existing formalized conjectures in the repository and its contribution conventions; this issue names no file, test, or entry point. Formalize the Erdős Problem 608 statement and verify that the resulting contribution matches the repository's established style and checks.

Written by the indexing model from the issue text.