For my science experiment, I am testing 3 people's typing speeds with 5 different instruments each. How do I find the best instrument that they improved on the most, even though each person has a different instrument that they improved on the most?

It must be one of three that they improved on the most, but you can't pick which of the three unless you have specific data on the speeds. I would hope you are controlling the factors related to the data being typed.