if only one of the 6 is correct, and you choose randomly, and the outcome of each round is independant of the other rounds, then...

...You are describing a case of the binomial distribution.

With the following:

probability of success (p) = 1/6

probability of failure (q) = 5/6

number of trials (n) = 32

the chance of getting exactly X guesses right is given by the formula

if you want to work out the chance of getting a range of values (5-10) then add up the chance of getting 5,6,7,8,9,10.

There are online tools that calculate these for you: Binomial Calculator