Totally agree with Ratzer.
It can be done, but not only will you have to train hard, you will need to know what you are doing and train in a very effective manner. My guess is that you will probably get injured in the process.
I managed to improve my 10k from 44:25 to 39:03 in just three months several years ago, but I suspect that my circumstances were quite different from you.
Incidently, it took a further nine months to improve that 39:03 to 38:58!!!
So in answer to your second question it would allow 6-9 months to improve your current 10k by 5mins.