I submitted an application to U Michigan with five LoRs. The minimum required was 3. One of these was from my thesis supervisor (should be strong), one from a professor I did some research with (should be strong too), one with a professor I've done four courses with (who knows me well, did course projects, should be strong but not in my field of interest), one a professor of applied math (did 3 courses with him, all with excellent grades, glowing recommendation, but applied math professor) and one from the director of my institute (renowned mathematician, did 2 courses under him, but letter may be generic, he may be too busy to write a strong letter). Did I do a wrong thing by submitting five letters? Please tell me. If that was inappropriate, I won't do so in my other pending applications.