On a very basic level, if you have five mouthpieces there is a pretty good chance at least one of them is a decent mouthpiece.
In my own case, I believe I probably passed the five mouthpiece threshold by my freshman year (!) of college. As a teacher I have observed way too many good students slogging along on some obviously brand X not good mouthpiece and that is all they have. Ignorance can be bliss, but it is not a good thing when it comes to your horn playing and equipment.
Why five is the number is with that many handy to try you will have some perspective that some really are better than others; it will open your eyes to several realities. One big one is that better equipment will help you play better, your problems are not all you but rather are influenced by the equipment.
The other thing that scares me is that I know there are teachers out there that have studios of students but have hardly any mouthpieces or experience with different mouthpieces. This is a handicap to good teaching, as you have no idea what the problems are that your students are having playing as they play along on potentially oddball and difficult to use equipment. One size does not fit all!
Not to mention that some of the best mouthpieces ever produced are on the market today, there are wonderful new models on the market. Take the plunge! Buy a couple mouthpieces. I have a few suggestions in this article in the ASU studio site.