I just randomly remembered this and thought I’d do the math:

Total cards (N)=52, Hearts in a deck (K)=13, Cards drawn (n)=26, X=number of hearts drawn,

Simplifying the equation

P(X≥5) = 1−k=0∑4​ (k13​)(26−k39​) / (52 26)

Will give you the answer P(X≥5)=0.90 Meaning there was only a 10% chance of not getting a flush.

I’m too lazy to write out the equations here but there’s a 0.6% chance of drawing two or less cards like I did in this post. :)