"5 things the egg industry doesn't tell you". Grammar question, the subject is "things or "the egg industry"? Use don't or doesn't?

Think of it this way...,

The Egg Industry does not tell you 5 things.

It should make it easier for you.

Subject is Industry, and Industry does, (you don't say Industry do).

The egg industry is the subject, so the verb should be doesn't.

Most style guides suggest that sentences should not start with a numeral and numbers under ten (or twenty) should be spelled out wherever they occur.

"5 things the egg industry doesn't tell you"
Things is the subject Things is plural so use "don't"
Eg "5 things I had to take on a camping trip were: a tent, a torch, food, water and a sleeping bag,

Doesn't. The Egg Industry is singular.

"Doesn't". It is the industry (singular) which is doing the telling.

It isn't a sentence, so it has no subject. The entire phrase serves as a noun. However, within the nounal phrase, there is a relative clause which does have a subject.

"Five things (that) the egg industry doesn't tell you..."

In what you've written "that" is left implied. Implied or not, however, it is still there. "That" is a pronoun introducing a restrictive relative clause. It means it's not any five things but is restricted to those five things that the egg industry doesn't tell you. In the restrictive relative clause, "egg industry" is the subject of the clause.

Don't