What is the mass of air in a room measuring 5m X 10m X 10m?

In order to find the answer to this question, you need to know the following equation:

m = dv

Where m is mass, d is density, and v is volume.  In this case, you are looking for mass, you have volume.  So you need to know the density of air.

As is turns out, the approximate density of air at sea level (and at 20 C) is 1.2 kilograms per cubic meter.

First, we must find the the volume of the room, which you get by multiplying its dimensions.  That tells us that the room is 500 m^3.  Now we can plug in the numbers

m = 500*1.2

Which gives us

m = 600 kilograms.

So, the air in your room weighs approximately (depending on how wet it is, what temperature, etc) 600 kg.