One epoch consists of one full training cycle on the training set. Once every sample in the set is seen, you start again – marking the beginning of the 2nd epoch.
This has nothing to do with batch or online training per se. Batch means that you update once at the end of the epoch (after every sample is seen, i.e. #epoch updates) and online that you update after each sample (#samples * #epoch updates).
You can’t be sure if 5 epochs or 500 is enough for convergence since it will vary from data to data. You can stop training when the error converges or gets lower than a certain threshold. This also goes into the territory of preventing overfitting. You can read up on early stopping and cross-validation regarding that.