Probability Problem (non-poker)

[RocketManJames]

For those who like puzzles/problems...

A friend gave me a probability puzzle to solve. I was able to come up with a 'simplified' formula that must hold true at the right answer, but I had to iterate using a computer to solve it. Is there a way to solve the following problem simply and without having to iterate?

Z placed a box on the table and told X to take out five balls from it (X didn't know anything about their colour/number). He removed five blue balls. Surprised, Z exclaimed: “That that would happen was an exact 50-50 chance.” What is the smallest number of balls and how many of them blue should he have placed in the box to get that result?

I will post my 'iterated answer' with my reasoning in a separate post.

-RMJ