How to select between letters of recommendation It's application season again. I've been a postdoc for two years and that is wrapping up soon. I'm applying for both permanent and postdoctoral positions, mainly through mathjobs.org. Many position advertisements ask for specifically three or four letters of recommendation, often specifying that one letter address teaching. My question is: what should be the pecking order if I must choose a subset of the letters I have?

I have five letters of recommendation on hand:


My thesis advisor
My current postdoc supervisor
A letter addressing teaching (an instructor at my graduate school department; I taught a stand-alone course that this person was the coordinator for)
A well-known, senior mathematician in the field from a prestigious university (this person knows me personally less well than the others)
A mid-career but well-respected mathematician at another university who I've visited


I assume all the letters are quite positive, although there might be some uncertainty for letter (4). If there are other factors that could tip things one way or the other, what are they? (Since this is a public forum, I can't be too specific about things here.) 

Another approach could be to simply submit all the letters of recommendation and let the hiring committee decide what to do with them. Is this a reasonable idea?
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).