Five weeks is great. We did a four week drive tour of Wales and England in 2017 that was one of our best trips ever.
Here are some tips that may assist in planning for your driving on your tour.
1) You will make better time on the express highways (we call them interstates in the USA, autobahns in Germany) but you won't see the scenic places so much. When you do take the back roads, you travel time will increase. There will be areas that you want to do the fast moving and others where you want more scenic.
2) Parking is a huge issue, especially in larger cities. You may wish to not rent one car, but split up your car rentals, when you are in a large city. Parking may cost you a lot and limit where you can stay. We didn't visit London or a major city (Cardiff and York were our largest cities), so we found parking most everywhere that was free with our small hotels or B&Bs. Have coins so you can pay for parking or the toilet.
3) Try not to plan a drive from one city to the next that takes more than 2 hours. We did that pretty well, however, we did have three days of our 28 where we did 4-5 hour drives. I found a great book Back Roads of Britain that helped me immensely. Perhaps there are Back Roads books of Portugal and Spain.
4) If you are going in September, you need to start booking ASAP, but AFTER you do your research. I love TripAdvisor which has a feature that allows you to check hotels in a city on a map that allows you to hold the cursor over the hotel location and it gives the price.
5) Car rental, recommend making sure your car can hold the luggage you will take. Also, get a navigation system with the car or have a GPS with the Europe maps.
Your route would start in Portugal. You will love this country, the people are just wonderful and while I love Spain, Portugal is just a notch above for friendliness.
I would plan on 7-8 days in Portugal, 14 in Spain and the rest in Italy.
LISBON
3 days in Lisbon to see the city, add more days for day trips to Evora and Sintra. After that, head up to Porto and stop in Obidos (small city with ancient Roman walls). Then to Nazare on the coast. There is a beach there. Then to Porto. 2 days in Porto.
The In Patio Guesthouse is wonderful, if you can get a room there, it is the very best B&B ever. Parking may be an issue, but this place is special.
Then head east up the Douro River Valley, very scenic with hills filed with vineyards. Then into Spain at Salamanca. You could stay there, then head toward Madrid, stopping in Segovia on the way.
Consider dropping your car in Madrid, your won't need one there and picking up another after 3-4 days in Madrid. Toledo, a few miles south of Madrid is a must (it was the ancient capitol of Spain). You can do it on a day trip from Madrid on the train.
Next, head down to Seville (this city is a must see), plan on 3 days there minimum. If you have time stop in Cordoba either in route, before or after Seville. You might even spend one night there. Head to Granada to see that wonderful city and the Alhambra, minimum 2 nights.
Some may say go to Malaga and do the beach at the Costa del Sol. Sorry, we did that and weren't impressed by the beaches there. There are nicer beaches up around Barcelona.
((You can decide to skip Porto and the Douro Valley and Salamanca and head to Seville from Lisbon--then you could go to Madrid after Seville, Cordoba and Granada-- Take at look at what time you have for Portugal and Spain. Porto is great, but you can always come back if you decide to do it this way))
Next Barcelona. Plan on 3-4 days there and more if you stop at the beaches in the area. Again, you don't want to have to pay for parking your rental car, so consider dropping your car here.
Not sure how you get to Italy, consider flying or a cruise (NCL has one from Barcelona to Rome--other cruise lines as well as ferries))
Rome, plan on 4-5 days there. continued