As you are staying 5 days in Lisbon, I think it would be nice to go to Porto. It´s our second big town, with a lot of historical places, the Oporto wine cellars, really a fantastic city. You can stroll near the Douro river (the old "Ribeira" quarter), see the baroque churches with "azulejos", and a lot more of things to do. Also the food in Porto is fantastic. Near this town is the Douro valley, where they produce the Oporto wine with superb views, a World Heritage from Unesco.

The only problem is that one day to go from Lisbon to Porto and see some interesting things in this town is very, very short.

As you probably will go to Seville after leaving Lisbon, going south, the better option is the Algarve where you will find nice beaches and some lovely small towns as Lagos (the one I prefer) or Tavira, another good option.

But in my opinion, the most interesting historical places are in the north of Portugal, not in the south (some places in Alentejo, like Evora, are also full of history).

But staying in Lisbon, going to Algarve and return again to Lisbon is not a very good idea if you go afterwards to Seville.

I think near Lisbon you have nice places to see like Tomar (a lot of history since the beginning of the Portuguese nation, the Templars.) or Alcobaça with a nice gothic church, Obidos a very small and nice village or Ericeira, a small fishing village.

I hope you have a good stay in Portugal, Helena in Lisbon