While I will agree that setting yourself up to get to all the notes easily is always best, and timbre should always be taken into consideration, I get what the teacher was saying. In the end, all that matters is that you play the right note at the right time. You don't always get enough time to assess the proper position when you're sightreading charts on a gig, and I've made pretzels out of my fingers on occasion. But all anyone cared about was that I hit the note, and I always managed to do it...well, not always...once in a while I goofed it goodWhoever "taught" you that was ill-equipped for teaching. Position matters quite a lot when you grow beyond early-intermediate playing, and not only for the physical act of getting from one note to the next, though that's bloody important. Timbre and feel are also affected by your selection of string/fret for that Eb. Second string first fret sounds quite different from third string sixth fret and from fourth string eleventh fret. There will be times when one aspect of playing outweighs others, such as being slightly off with your timbre or pitch vs. being way off with your timing, as an example. You'll be the one to decide which is the lesser of the evils; which one will more likely earn the stinkeye from the BL/MD.
The only reason the bands that I've worked with ever require a 5 is for doing "Uptown Funk" by Bruno Mars. I've got a Hipshot double stop XTender on my E string that I can tune to drop D or B, and that always satisfies anyone's occasional need for those low notes. But I can't do "Uptown Funk" on anything but a 5 and have it come out sounding good. Other than that I've done a grat job avoiding it.I play with horns more often than not and have never felt need of a five-string. I know that a lot of players disagree but their arguments haven't been compelling.