I need a quick algorithm to select 5 random elements from a generic list. For example, I'd like to get 5 random elements from a List<string>
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Iterate through and for each element make the probability of selection = (number needed)/(number left)
So if you had 40 items, the first would have a 5/40 chance of being selected. If it is, the next has a 4/39 chance, otherwise it has a 5/39 chance. By the time you get to the end you will have your 5 items, and often you'll have all of them before that.
This technique is called selection sampling, a special case of Reservoir Sampling. It's similar in performance to shuffling the input, but of course allows the sample to be generated without modifying the original data.