You have absolutely done the right thing in refusing to get up at 5 am to help your mother with the test. Why on earth would she need to do it that early?

I recognise this helplessness from both my mum and my grandmother. I think my granddad did everything for my grandma so she never learned to do things on her own. Never had any interest in it either. When he died, her kids took over in basically managing her life.
I suspect maybe my mum has learned that behaviour from my grandma (her mother). Both of them are very quick to say something is too complicated for them without even giving it a try.

Not sure if this is much help because I absolutely cannot understand it, but there are several possible underlying issues that might cause it. Anxiety, low self esteem, motivation issues.

It's very frustrating watching someone act so helpless without even trying. But if they don't see they have a problem, all you can do it set boundaries for yourself, keep taking care of yourself and do not get lost in taking care of them.