Dubai is a city that was mostly invented in your parents' lifetime. It began in the early 1700s as a small pearling and fishing settlement on a creek, became a free trading port in 1901, and then spent a few decades turning modest oil money into airports, towers and islands shaped like palm trees. Today about 92% of the population are foreigners, and the skyline holds the tallest building in the world.
That makes it easy to mock and hard to skip. The honest version is this: Dubai is two cities. One is the Creek, where wooden boats still carry people across the water for a dirham and the souks smell of saffron and frankincense. The other is a stretch of coast with the Burj Khalifa, the Marina and the Palm, built to be impressive and air-conditioned. You want both, plus a night in the desert, and that is why five days works. Three leave you running between towers. Five let you sit on a beach, take the slow boat and still have a free evening.
The plan keeps each day in one part of the city. Day one is Downtown with the Burj Khalifa and the fountain, day two Old Dubai on both sides of the Creek, day three Jumeirah with the beach and the Madinat, day four the Marina, JBR and the Palm, and day five the Dubai Frame and a desert safari. Sharjah, Abu Dhabi, Hatta and the mountains of Ras Al Khaimah wait under If you have more time. Read the notes on the United Arab Emirates before you land, and if you can, start on a Monday: the Jumeirah Mosque has no visits on Fridays, the souks open only from about 4 pm that day, and Friday suits the desert day best.