Reaction time test high score

Hi everyone.
I am making a very simple reaction time test for arduino. I have made a lot of the program and the only thing left is making a high score board. I can't really figure out how to make it.
The reaction test makes you take the test 5 times and then it averages the time and that's your score. I want it to be able to read all of the current high scores and then figure out, if your last score should be on the high score.
I hope you can give me some pointers.
Thanks a lot.

Sorry for being pedantic, but if it is a reaction time test, then isn't it a low score that you want to save?

You are right, but you do know what I mean.