How to select between letters of recommendation
On mathjobs, you can choose which letters to send to which schools.  

For research-oriented jobs, send all those letters, assuming those are the established people in the best position to evaluate your research and teaching abilities.  Five is a good number of letters.  Three is on the low end, even if that is all that is asked for.  Most people submit 4-6 letters.  (On the other hand 10 is too many.)

For primarily teaching-oriented jobs, you might try to get 2 teaching letters and 2 other letters (which can address some combination of research/service/collegiality).  At least one of the teaching letters should be from someone who's observed you teach recently.  This latter aspect is also preferable but not required for many research-schools (for tenure-track positions, not so much for postdocs, even if the postdoc involves teaching).