5GHz wavelength = 5.99584916 cm. The spacing of a Faraday cage has to be < 1/10th the wavelength you want to block. So for 5GHz that's 0.599584916 cm or 5.99584916 mm or less.
The cage material has to be made of a conductor like copper or silver. And it would probably have to be grounded too.
A 3m x 3m x 3m room is 54 sq m. You'd need about 791 sheets of the copper 0.63mm mesh + staples to nail is to the walls. Minus the area of the door. Cost about $6,328 + tax.
At 5GHz the skin depth is pretty shallow; in units(1), sqrt(2 / copperconductivity 2 pi 5 GHz mu0) says 0.93 microns. I think you could probably get by with 3 microns of copper vacuum-deposited on Mylar or on fiberglass window screen.
Steel window screen coated in copper might work even better and could be made by electroplating first a nickel flash and then the copper layer, avoiding the expense of vacuum coating. I'm not clear enough on the physics to be sure, and maybe it would be worse, but the skin depth in even ordinary steel is about an order of magnitude smaller because of its magnetic permeability.
"Booster bags" for shoplifting use (ungrounded!) aluminum foil. I think the reason they have to be several layers thick is that anti-shoplifting RFID tags operate at a much lower frequency, and aluminum foil is typically only 10 microns thick.
The cage material has to be made of a conductor like copper or silver. And it would probably have to be grounded too.
This website sells copper mesh with 0.63mm size 150mm x 455mm for £6.05 + tax (~$8 US). https://modelshop.co.uk/Shop/Item/Copper-mesh-woven/ITM6558
A 3m x 3m x 3m room is 54 sq m. You'd need about 791 sheets of the copper 0.63mm mesh + staples to nail is to the walls. Minus the area of the door. Cost about $6,328 + tax.