(Why five? how
many fingers you got?)
Don't know if that was the real reason, more important probably was the
fact the 5 bits could
code up to 32 symbols, sufficient for the alphabet.
I believe the original Baudot telegraph (probably the first device to use
a 5 bit character code) used a 5 key chording keyboard, but I seem to
recall you used both hands on it (3 fingers of 1 hand, 2 of the other).
The fact that 5 bits allows the complete alphabet is probably the real
reason...
-tony