Would it be better to stay in Seville as a base camp and do day trips. We plan on seeing Granada and Cordoba. We have 5 days in Seville.
Will you be renting a vehicle or taking trains or buses? Cordoba is an easy day trip from Seville but I wouldn't attempt Granada. With the distance involved and the amount of time necessary to really see Granada you should stay there for at least 2 nights. What is the purpose of a base camp? Do you have a friend's place lined up for free? Need a bit more info to be of help.....
With 5 days I would spend 3 in Seville and 2 in Granada.
Cordoba would work (but you will pay more for your room in Seville than Cordoba). Granada is too far away to be a reasonable day trip option (three hour driving time each way). It won't leave enough time to do justice to the Alhambra, let alone anything else.