Tough Decision for me

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I have a cat who was born of another cat that I picked up off the side of the road.. Now I haven't got very much money and what I do have goes to food,(people and pets)bills, cat litter etc. Anyway this cat that I have got pregnant because I couldn't pay off my vet bill for my dog that I lost in May(He was twelve and very dear to me so I did all I could to save him)anyway she had her kittens so now I have five cats, five kittens and a dog.. I have only found one home for one kitten , I have had offers from farms but refuse to send my cats or kittens to live in forty below weather outside so they can be breeding machine until they die.. What I am going to do is to take her and the four remaining babies to the shelter as I feel this way they will be spayed/neutered given their vaccinations and someone will have to pay to adopt them rather then just get them for free.. I am asking opinions on this.. I cant keep the female as she is very young and not a good mother cat and she lost way too much weight while nursing I do not want for her sake to let her breed again, not mention that I really don't want to be adding to the already way too large unwanted cat population.. What would you do in my situation? Please no bashing I really love my animals and this is very difficult for me.