Not likely to be just the cable. You'll need to repair (AndrewWynn has a method on this) or replace the whole door handle carrier. I've now replaced all 4 of these on my 2001, all with Febi parts, all fitting well and with no problems.

The common failure point is a little U in the Aluminum casting that holds the pivot in place. This eventually breaks off and the handle does nothing. But sometimes before that, only one side of the U breaks and the other side just bends a little, so you have to pull the handle further out.

You might want to replace both sides, or at least feel for how they feel.

Also, while you're in there, inspect the window regulators - another current thread on that. I swear, the door components on these cars ...

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2001 X5 3.0i, 203k miles, AT, owned since 2014