If you only had 5 days in this little, but diverse country, Id recommend flying into Quito.
Once in Quito see the colonial old town, the best in Ecuador, then go up the teleferico (cable car) which has some spectacular views and a nice hiking trail.
Then be sure to go out partying in EL MARISCAL nightlife district, the TOP place to party, see and be seen in Ecuador.
After 2 days and 2 nights in Quito head south to Latacunga where you can see Quilotoa and Cotopaxi Volcano. Amazing area. 1 Day Bike tours are available from Quito.
From there continue south to Baños, a neat place to eat well and live cheap for a few days. Adventure sports like rafting, hiking and biking also abound.
After Baños Id head to Puyo 60 km away, which is at the mouth of the Amazon Jungle so at least you can get a small taste of what life is like in that region of Ecuador.
Then back 4 hrs to Quito.
Thats what Id do if I had 5 days in Ecuador.
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