128 bits are 16 bytes, which is at best a binary string of 16 characters. Remove some bits for the not random parts of the UUID and still you don't get down to 5 characters. Furthermore "a 5 character a-z random string" is less than 5 bits per character. Make them less than 6 by adding A-Z and the ten digits.

About storage, at least PostgreSQL has been using 16 bits of storage since at least version 8 many years ago.

https://www.postgresql.org/docs/current/datatype-uuid.html

https://www.jacoelho.com/blog/2021/06/postgresql-uuid-vs-tex...