Break-even fee for opening boxes

One of five boxes contains $150 and the other four are empty. You pay a fixed fee of $X$ dollars each time you open a box, and you keep opening boxes (in some order) until you find the money. What fee $X$ makes this a fair game?

$50. The money is equally likely to be in the 1st, 2nd, …, 5th box you open, so you pay for $\tfrac{1+2+3+4+5}{5}=3$ boxes on average. Fairness needs $3X=150$.