wireless connection over multiple stories/floors

I have been asked to set up a wireless network in an apartment block of 5 stories high.
Currently there is a Wifi router on the ground floor, it is not visible on the floors above. I need to connect all floors to the wifi router. I have seen this in on hotel before, where ther router have a chain of antenae connected via CAT5/6.

There is an access box to pipes/cables that runs from the ground floor to the top floor, so the access for cabling in very possible.

What equipment would I need, router and cables/antenae to create a chain such as this? I know it is possible, but not sure what the antenas type are called.

Any pointers would be much appreciated.

Ubiquiti's UniFi was designed for this type of use.

a few options really, how many apartments on each floor/ what is the rough floor area of each storey?

If cable runs up aren't too much on an issue then it should be relatively straight forward, just need to address which vendor to suit the coverage area, throughput requirment and cost!