It's so heartbreaking to watch someone struggle with depression…and it's far worse when you feel powerless to help. First off, I have to say that you should NOT feel guilty
That said, your mother does sound very depressed. Getting out of the house for fresh air, exercise, and social activities with others are all helpful, but when someone's depressed, it's sometimes nearly impossible to get the energy of activation needed to do those things.
What I'd suggest is sitting down with your mother and asking her what she thinks would help. She might not have any answers for you -- depressed people often feel completely hopeless -- but it's a good place to start. Is there any way she'd be receptive to trying antidepressant medication, talk therapy, or both? I know you live far away, but could you possible arrange to go with her to see her doctor? It might be difficult for her to broach the subject of seeking help, and having you with her might make it easier.
I wish you both the best of luck. Hang in there, and be sure to take care of yourself, too. Caring for a depressed person can seriously zap your energy, even if you are five hours away.
about living your own life. And you shouldn't feel that you're responsible for your mother's happiness or lack thereof. I know that's much easier said than done, but please stop beating yourself up.