any air purifier will definitely help. as itself with the most basic of basic will act like a dust filter. like a slow vacuum cleaner.
construction dust are dangerous. they also have chemical dust. 5th floor will be affected when its carried by the wind. also, you walk through the ground floor everyday, in/out, you will carry external contaminants.

i agree with you, try a affordable one first.

one of the best way till construction complete is, get air purifier, buy NASA top recommend three plants for internal air circulation, and don't open windows except on rainy or windy days from other direction. the hardest to die and most easy to maintain is "money plant", soil based or water based also can.