What are the odds of spinning matching items in a slot machine? Lets say we have a slot machine with $5$ reels. Each reel has $5$ different items on it.
What are the odds of spinning $2, 3, 4$ and $5$ matching items?
As I understand the probability of rolling a particular item in each reel is $\frac15$. I just don't know how to calculate the combined probability of these events. Is it simply $\frac15\cdot\frac15$ for two matching items or are things more complicated?

Yes but you need to multiply $1/25$ with $\binom 5r, r=\{2,3,4,5\}$ as you need to consider permutations of an arrangements on 5 distinct reels and hence consider choosing any two reels to be possible in multiple ways, i.e. $\binom 5r$ 
