Comprehensive way to indicate error code using single LED
I have used a lock-in amplifier which would blink out its IP address using a single LED. It would flash 1-10 times to encode each decimal digit, with gaps between digits and longer gaps for the groups.  It didn't work very well, watching and writing it down was quite error prone.  Fortunately you have 5 bits not 32 bits, so it should be easier. Suggestions:


You are trying to communicate 5 bits, not a 5-bit number, so sending it in binary (as you have suggested) is a good idea.  If you were sending a number from 0 to 32, with 32 different meanings, you could consider decimal or octal or similar.
Representing bits with long and short flashes might be easier than one/two flashes.
Five bits is not too many, so it should be possible for the user to remember all of them, without stopping half way to write them down. This means they can go faster than you've suggested.


My initial solution would be to have five flashes, at half second intervals, then a one to two second wait, then repeat.  This means that a 0 would be represented by 100ms on, 400ms off, and a 1 would be represented by 400ms on, 100ms off. If I was then using such an interface as a customer, I'd probably watch the light for a few repeats whilst muttering to myself "long, long, short long, short", until I was sure I had the right pattern, then write it down and look it up.