Assume that I built a 2TB RAID 5 array, and it's running and some data is stored on it.
Now I need to increase its size to 5TB.
Can I increase capacity, particularly by adding extra drives? How?
If yes, is it possible to do this while the RAID array is running?
Yes, you can increase it adding more disks
Yes, you can do that with it turned on. But it depends a lot on the hardware that's running it. In general you add another drive, send some command so that the controller redistribute all the data using it, and you're done.
And just adding HDs of the same size can make you need much more drives, you could consider replacing them.