We went through a similar situation with our Mu Mu. We had only had her a few weeks (the wife got her from a chain pet store before we knew any better) when she started having breathing issues. We took her to the vet who told us she only had a small amount of clear lung space, plus a mass in her stomach and a possible liver infection and was unlikely to recover. We opted to nebulize her and give her Cipro rather than let the vet euthanize her there and then but despite our best efforts and a brief spell where she seemed to be getting better she eventually refused to eat and only lasted a couple of days before she died in my hands.
I still feel incredibly guilty that we didn't do more but take solace that at least she had some happy times with us and was loved and cared for before she passed rather than being stuck in the pet store.
I keep beating myself up over it wishing I could have none more but realistically I am not sure what else we could have done as she hid her illness really well right to the end, she was running around and popcorning like crazy only a few days before.
When I would put my hand in her cage she would rest her paws on it and just sit there like that for ages.
She was sat with me on the sofa right before she passed, on a cushion next to me, but got up and walked across on to my lap and settled there for a while before climbing up on to my shoulder. I then felt her tense getting ready to jump (which would have been a bad idea from that height and would have been fatal or at least caused serious injury) so I grabbed her to stop her and she freaked out so I put her back in my lap but she was very weak. I tried to see if she would take some critical care but she wouldn't and didn't want any water either and her breathing got shallower and shallower before she eventually passed cradled in my hands. I think she knew she didn't have long left and that's why she wanted to be in my lap. I wish I could have saved her but if she was going to go I would rather she went that way than alone and unloved in a pet store.
As others have said you gave her 5 months of love and life she would otherwise have not had, I am sure she loved you for that.
May she rest in peace.