When a cow or horse collapses and doesn't get treated by a vet, chances for death are very high. Problem is that, in this state, even a vet can't do much - the cow could be operated on if a cause was known or highly suspected - again nothing an ordinary person could do due to lack of instruments, knowledge and skill, for a start.
Not eating food for an animal that usually eats all day is a great sign of pain. So, for a starter, the question you could ask yourself is: can I remove the source of pain? Sadly, in most cases the answer will be no. A cow not eating soon is a dead cow, and the lying down will do them in within days. Unlike men, many animals can die very soon from lying down. They are so heavy that their own weight often damages something inside if they struggle to change the lying position. So the next question you should ask yourself is: even if I get the cow to eat, will I get her to stand in a reasonable amount of time? If the answer is no, we still got a dead cow in the end. Next thing important to know is: if you got a heavy animal like a cow, which is also by species not known for very long sleeps, chances are high that even if the animal started eating and could stand once it raised, the muscles and joints might already so stiff the animal will not be able to lift its own weight up. Take horses, for example: I've seen quite some healty horses that somehow got stuck over night, and they are healthy, but once they have been down all night (which is very long for these animals!), even the most healthy ones sometimes struggle to get up by themselves.
Sometimes farmers try to lift the fallen animal up with a tractor (or similar), which might help it stand when it is strong enough to stand but not strong enough to stand up. If you got a cow that would stand and graze after being lifted up, there are chances it might survive. Still, if cows are too weak to stand up, they often suffer and don't have long to live, no matter how hard you try to help. Sadly I've seen such uplifted animals (cows/horses), and none of them survived even though they got proper, and in one case really intensive medical care, and often they wouldn't even stand for more than few hours until lying down again (which they would not do purposely; they know pretty well they will not get up once they lay down, but the pain and weakness will make them do it!)
I will not judge about whether anything should be done at all, including whether the animal should be put to mercy or not. No remote advice could answer such questions in general and thus shouldn't be taken as fact.
If you find a malnourished cow which is unable to move, I'd agree with the vet that the cow probably will not survive more than three days, so I simply see no way how your question of nursing the cow to recovery could be answered. Fortunately, a 5 month old calf should be old enough to survive without its mother, so, for anyone who sees himself in a similar situation, a good addition to the question would be: should I help the calf when the mother has died.
I hope this might help someone someday, if only to understand the big picture.