We visited Madrid, Seville, and Cordoba last year, and Barcelona, Granada, Cadiz, and some other places this year - but never with a 5 yr old in tow.
What did most appeal to us about much of Spain was the FOOD culture, and for sure, as mentioned in another post above, much of that is an evening or night time activity, so keep that in mind with a child. We loved heading out in the late evening and how alive the streets and restaurants and bars were with folks out and about - especially in Seville where it was so pedestrian friendly around the main cathedral. Barcelona was much the same - lots of pedestrian friendly areas that are good for strollers and bars/restaurants really bustling as the evening wore on. We could find places to eat at "normal" US times, but we jumped into their later eating hours and were happy we could.
One thing that you should think about is that much of "historic" sections of Spanish cities are cobbled, and Spain in general is deceptively VERY HILLY. We were generally hitting 20,000-40,000 steps a day (A LOT even for us), and the walking wasn't the tough part - it was the uneven (sometimes slippery) surfaces and the hills. We seemed to always be walking up or down, never flat. Granada was insanely hilly - especially for the Alhambra section, so be prepared for that if pushing a stroller. There always seem to be shuttles or buses or other, so you may just get around using them :)
And kids are EVERYWHERE so you can probably just do what those local folks do. I saw some stroller storage at sites, but can't say I paid much attention to it.
When we were in Cadiz, we did a side trip to Jerez for the horse show there. That might be really nice for a 5yr old. We saw plenty of young kids in the audience, and kids love horses, so a trip to Jerez for the horse show (and the stables & coach tour) would be a recommendation.
As a side note, in Granada, we saw our one rare purse snatching right in the main cathedral area. I'm not sure how you "lock down" your stroller and stuff while paying attention to everything else, so keep that in mind as you are planning what you are bringing and how you will manage it all. Spain is safe, but crimes of opportunity are possible in the big tourist parts of town.
To your main question - assessing your itinerary - I might say it just seems "long" for a trip with your daughter. For me and my wife (50 yr olds), it seems like a great mix, and we could easily fill those days with things. I just don't know that I would be able to do that with a small child, but probably it would mean paring things down from our usual many different activities per day down to one "big" item a day, and the rest more about eating, resting, sitting/playing in a park, and enjoying just being present there. Spain has some really FUN playgrounds for kids (and adults). You don't mention Valencia, but the wide green park running through the center of town is a great place to take a kid, and you might consider a stop in Valencia instead of somewhere else or drop Cordoba (a day trip there from Seville instead is probably sufficient).
