Short answer
Five days covers Dubai and Abu Dhabi together: three days in Dubai for the Burj Khalifa, the desert safari, the Marina and the old souks, one full day in Abu Dhabi for the Sheikh Zayed Mosque and Louvre Abu Dhabi, and one for a theme park or the beach. Four days covers Dubai alone.
Dubai is compact and the metro works, but distances still eat time. Downtown to the Marina is 25 minutes without traffic and 50 with it, and Dubai to Abu Dhabi is a 90-minute drive each way, which is why the Abu Dhabi day needs to be a full day rather than an afternoon.
Three days in Dubai is the honest minimum for the headline sights: Burj Khalifa's 124th-floor deck, Dubai Mall and the fountain, the abra crossing to Deira for the gold and spice souks, an evening desert safari with dune bashing and dinner, and Palm Jumeirah with the View at the Palm.
Beyond five days you are adding theme parks — IMG Worlds, Motiongate, Atlantis Aquaventure — or a day trip to Hatta or Sharjah. Families with children generally use the extra days well. Couples usually find four to five days sufficient, and June to September heat of 42 to 48°C shortens what anyone wants to do outdoors.