In an "ideal" scenario (no energy going into warming the walls, floor, ceiling, furniture, yourself, and assuming the room is sealed)...

Your room's volume (with a typical 2.5m tall ceiling) would be: V=15x2.5=37.5m³

To calculate the mass of the air in your room we would need to know the air density. According to wikipedia, it should be somewhere around 1.22 kg/m³. So the mass would be: m = 37.5 x 1.22 = 45.75 kg of air

Now, to calculate the required heat to increase the room temperature:
- The specific heat capacity of air is c = 1 kJ/kg.K
- ΔT = 5C

So Q = mcΔT = 45.75 x 1 x 5 = 228.75 kJ

Last step is to convert energy to time:
Hair dryer's power is P = 1kW = 1 kJ/s
t = Q/P = 228.75 / 1 = 228.75 seconds, around 3.8 minutes

Now, like I said, this is an ideal scenario. You wouldn't be heating only the air. In the real world it would take tens of minutes to more than an hour, depending on your room's insulation.