Difference between core i3 and core i5?

It's been a while since I've had to shop and play with different computers, so I'm a bit out of phase with the latest Intel processors. My friend is asking me if she should get a core i3 or i5 for her mom. The user's needs are Internet and writing, but I suspect there'll be heavy youtube usage and some medium multi-tasking.

Would a core i3 be sufficient for this user's needs to save them money or should I recommend a core i5?