Green's Open Problems #74

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.74

What is the largest subset of $[N]^d$ with no 5 points on a 2-plane?

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-05
* ams-52

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

Start with the linked Green's Open Problems PDF and read problem 74 carefully, then inspect the formal-conjectures repository for conventions around stating mathematical conjectures in Lean. Formalize the conjecture that asks for the largest subset of [N]^d with no five points on a 2-plane, with the finished statement fitting the repository's existing conventions.

Written by the indexing model from the issue text.