Like most Low Earth Orbits (LEOs), the satellites will probably eventually have their orbits decay and burn up in the Earth's atmosphere. How long, on average, would this take. I am assuming that there are zero factors other than gravity and aerodrag. So, how long can the SpaceX Starlink satellites survive before they deorbit?
Around 5 Years
Starlink satellites are launched into orbits between 335 and 354 miles above the Earth. SpaceX had originally planned to fly some of their constellation at 800 miles, but petitioned the FCC to change the architecture such that all their satellites fly below 380 miles. This was requested specifically to reduce the time it would take for a dead satellite to de-orbit.
SpaceX publishes a graph showing expected decay times as a function of altitude:
The reason I said 'around' 5 years is that decay times can be affected by solar storms and other factors, and the satellites will be at slightly different orbits. But that wouldn't affect decay times at that altitude very much.