Need advice on completing my Spain itinerary

Trying to figure out itinerary for next 7 nights. We are flying out of Madrid so will spend last two nights there. So, for remaining 5 nights, would love input.

Given the fact that you only have 5 nights to work with, I'd suggest something like this:

Fly from Barcelona to Granada (2N) then take train or bus to Sevilla (3N).

If you decide to skip Granada, then you could fly to Sevilla( 5N) and day trip to Córdoba and Jerez de la Frontera.

Unfortunately you don't really have time to travel to Gibraltar.

I'd not recommend taking a day trip to Granada, from Sevilla, as this journey takes 3 hours each way.

BTW, August is the hottest month in Andalucía, so if you haven't booked your flights, you may consider waiting till October for better weather.

Happy 25th anniversary!

Seville's average high in August is over 100F.

Personally, i think Barcelona could do with more time, then any leftover days could be spent in Madrid or day-tripping from that city. You have Segovia and Cuenca (latter needs early puchase of AVE tickets) in addition to Toledo. Barcelona has wonderful day-trip options, too. Weather stats will show you that Barcelona is likely to have much more moderate temperatures than Andalucia and somewhat cooler temps than Madrid.

Thanks for input so far. I had not considered a flight from Barcelona to Granada.

I don't mind the heat. We live in Sacramento, CA area and are used to it. In fact, Sacramento is actually on a lower latitude than Madrid!

Your first option consumes at least a day and a half in travel time.
Heat + masses of people = higher unhappiness potential
Before you attempting Granada you need to check on ticket availability for Alhambra
Suggestion:
Palma - 3
Barcelona - 4 - huge menu of opportunities
Seville (fly) - 4 - take a day trip via be to Ronda or train to Cordoba (very doable offering ez access and least amount of RT travel time)
Madrid - 2 - if art is your love then stick to the museums (which are air conditioned). Madrid has one of the smallest old historic districts embedded into the middle of a huge city
This itinerary allows a reasonable taste of four distinctive cultures within Spain while striving to minimize travel stress.

Rather than long day trips from Seville (Gibraltar, Granada are really too far) I would suggest easier ones from Madrid.

Day
1.2.3. Palma de Mallorca (3)
4.5.6. Barcelona (3)
7. Fly to Seville (3)
8. Seville sights
9. Day to Jerez
10. Via Cordoba to Madrid (4)
11. Madrid sights
12. Day to Toledo
13. Day to Segovia
14. Depart Madrid

For luggage storage in Cordoba when visiting the Mezquita and travelling onwards afterwards.
http://english.turismodecordoba.org/seccion/supervised-left-luggage-office---locker-cordoba

Thanks so much again for the very thoughtful replies! I have lots to think about!