Scoring System

Basically I need a formula to be able to do something like

=IF(AND(F5<B5,B5<H5) If true it outputs a cell with the score, if it's false it moves onto the next range to determine if it is classified under that. Here's an example. Also, is there a value for infinity?

Thanks.

Here's basically what I need simplified, you can still look at the example.
If x < 20 = 5 points
If 20 < x < 60 = 10 pts
If 60 < x = 15 pts.

Basically I need a formula that can do this. I think it's a simple solution but I just can't find the right function for it. Thanks again.