Getting around Andalucia

5 days is barely enough time for Granada, Seville and Cordoba.
The Alhambra is a full-day affair and it is too far from Seville to be a reasonable day trip. Plus, there is more to Granada than just the Alhambra.
From a logistics standpoint, it would make sense to spend 2 nights in Granada and 3 in Seville, leaving Granada early so as to get almost a full day in Seville. You could then visit Cordoba as a day trip from Seville.

The beach in Nerja is nothing special, and a day trip to Tangiers is a massive hassle, to stay polite. Hours on buses and ferries to be greeted by an army of touts on the other side of the straits of Gibraltar...

I agree on dismissing Tangier and Nerja. But since the Alhambra and Cordoba are your stated priorities, you could just visit those two and save Sevilla for a future trip. Something has to go.

There are fast trains between Madrid/Cordoba/Granada as well as between Madrid/Cordoba Seville and Seville/Cordoba/Granada. Seville alone is worth at least 3 full days (4 nights); Granada and Cordoba, two full days (3 nights) each.

Granada is over 150 miles from Seville, much too far for a good day-trip. There is more to see in Granada than the Alhambra, which can take more than half a day by itself. It's not hard at all to take trains between the major cities in most of Andalucia. (Yes, Ubeda and Baeza involve buses, but those are not typical destinations for first-time visitors to southern Spain.) And why take a tour to Cordoba that uses a bus when the train is so much faster? It's better to have the time in Cordoba.

Hello from Wisconsin,
Trying to see too much will make for a disappointing trip and certainly not a vacation. I don't want to sound or be harsh. I want you to enjoy Spain. Once you make your way to Spain, you will recognize that you can come back another time and a time after that.

Andalusia is a great place reflecting an ancient mix of people. Granada has the Alhambra and don't forget St. John's Basilica. Cordoba is just beautiful. The Mosque/Cathedral is all I wanted it to be. The streets are narrow and the Plazas plenty. The Roman bridge at dusk into night is a place to stay before you go to a late supper. And I would stop with that.

Seville is a different animal. I think it takes time to get into and enjoy Seville. It should be saved for your next trip and then include Baeza with the Theater Cafe.

Years ago Mrs. Smith of North Ireland refused to let us check out of her B&B because we were traveling too fast. I thank her every trip I have taken since. We thought her home town had little to see until we slowed down. That off the road place is of our most memorable stops in Ireland.

Packing too much into each day leaves you tired. And speaking of packing, less is more.

wayne iNWI

I would go from Madrid to Granada (2 nights minimum) then to Cordoba (minimum 2 nights), then to Barcelona, all by train (see below). The trains are fast and comfortable. Or if you're starting in Barcelona, then the opposite, of course.

Use the renfe.com site to see train schedules and prices. Train tickets get more expensive the closer you get to the date, so it's best to book well in advance if you are sure of your itinerary (these discounted tickets are not refundable).

Forget Tangier, it's a dirty, decrepit place (apart from the luxurious VIP gated communities in the hills) full of rip off merchants and hustlers. I get the feeling that many people just want to go simply to say that they've been to Africa. Stick to Spain.

I also don't understand the allure of Nerja. Why is it so popular? For a beach destination I would opt for Estepona over Nerja. Estepona has a fantastic old town situated adjacent to the coast with very attractive streets heavily decorated with flowers. It has more of a Spanish feel than Nerja which is quite touristy particularly the Balcony of Europe. Here is a site that weighs up the pros and cons of each town: https://www.cityorcity.com/nerja-or-estepona/

Thank you all for your insights.