Hi snahl - Welcome to Beoworld.
If you tell us where you are based it will help folk to recommend a potential repairer for your CD5500.
The CD50 does work with the BS5500 (in fact at the release of the BS5500 the CD50 was sold with it as the CD5500 wasn't available until a while later).
They do sound different, some say the CD50 has a more "analogue" sound although I'm sure it is down to personal preference. The CD5500 of course has a digital output which will work with the top of the range BL5's if that's important to you.
Both are now quite old and so will likely suffer hiccups from time to time but both are generally repairable - a good service normally works wonders.
Generally speaking, you aren't learning much if your lips are moving.