Tenerife is a volcano with a coastline attached. Teide stands 3,715 m high, the highest point in Spain, and its national park is the most visited in Spain and Europe, with more than four million visits a year. The Spanish took the island in 1496, the last of the Canaries to fall. Then tourism arrived in the south in the 1960s, and the island split into two personalities that don't much like each other.
The split is weather. The trade winds pile cloud against the north coast, which makes it green, mild and often gray in the morning, while the south sits in the rain shadow and gets sunshine most days. That is why this plan uses two bases: Costa Adeje for the beaches, the boats and the west, and Puerto de la Cruz for Teide's north side, the old towns and Anaga. Five days is right because the island is small on the map and slow on the road: plan on an average of 30 km/h, not the speed limit, and a rental car.
Days one and two cover the south and west: the Barranco del Infierno, a whale boat, Masca and the Los Gigantes cliffs. Day three crosses Teide National Park and ends in the north. Days four and five are the north coast, then Anaga's laurel forest, Santa Cruz and La Laguna. For the country as a whole, see Spain. Start on a Monday if you can: the plan then never lands on a Sunday, when most shops are shut and buses run less often.