What is different?

The first is present perfect tense, the second is past simple. 

Both mean that you did something five times in the past. Using present perfect generally would mean: - the fact that you’ve done it has some sort of relevance or effect on the present circumstance - or, especially, that you will be doing it again and are expressing that you’ve done it five times *so far* > I’ve driven my new car five times; I’m getting used to it. > I’ve driven my new car five times; I’ll drive it again tomorrow. Using past simple is a more neutral way of phrasing it; there’s no implications for the present. This is used especially when there’s a causal disconnect between the past events and the present. > I drove my new car five times last week. In North America, it is becoming more acceptable to use the simple past where other dialects would use the present perfect, but as of this moment, both are still in common use.

i’m an esl teacher, the books i work with tell students that: “i did something five times” is usually followed by a specific time, i did something five times last year “i’ve done something five times” covers your whole life, meaning you did the thing but when you did it it’s not relevant basically you completed something but one form cares about when you did it and the other doesn’t, like: i had pizza 3 times last week i’ve had pizza before (i tried it but i don’t tell you when)