One way of doing this: You should check the IC50 for 5FU of your cell line. E.G. by MTT after 3-6 days - so you will have an impression of how much drug your cells will tolerate.
Then you can start by treating the cells with the IC50 concentration with every change of media. If you find that it's too toxic, you can withdraw the drug until cells have recovered and then start treating again. Possibly you will have to adjust the dose. If you see that cells are growing fine again under drug pressure go up with the concentration (slightly and gradually) and proceed as above. You will get a feeling for it. If you increase the concentraion too fast you may lose all the cells, so better be safe than sorry. It may be helpful to use 2 or 3 cultures in parallel using different concentrations. This maybe take months - so be sure to freeze down backups whenever you feel you made progress.
Long-term exposure to 5-FU estabslies the resistant sub-population, but it is highly likely that resistant cells exhibit plasticity to become sensitive parental population. In the cultured cell line system, the epigenetic alterations rather than secondary genetic mutations are expected to be responsible for the acquisition of the resistance to 5-FU.