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Answer: 2 possibilities
$5^2 + 6^2 = 25+36=61$
$\therefore$ thrid side is $\sqrt{61}$
$6^2 - 5^2 = 36-25=11$
$\therefore$ thrid side is $\sqrt{11}$
Impossible since the hypotenuse should be the longest side
$\therefore$ there are only 2 possibilities.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.