Do be careful though, because even though it won't appear on your reference letter, a prospective employer could call a former employer for references and that could be another ball game.

Also to receive chômage/unemployment you must be considered "employable" at all times during your job search. I'm not sure of the parameters, but it's important to find out what the rules are if you are ill and on chômage at the same time.

Maybe your doctor could indicate that you are only able to work part time ? This way you could stay involved in your job and recuperate and get well.

5 days of sick leave in 24 years.... that's exceptional !
I wish you the very best, get well soon ! kindest regards and hang in there