Multi-story building.

[pizza]

Is there a general term for a multi-story building? 3~5~10 floors.

There is edifice, but I suspect is not a common word in spoken English.

[5jj]

There are no single words for a multi-storey (BrE) building as far as I know, except for skyscraper or tower, but they are much higher .

[ostap77]

There are no single words for a multi-storey (BrE) building as far as I know, except for skyscraper or tower, but they are much higher .

How about a high-rise bulding if there are only apartments and no offices? Or just a 10-storied building?

[emsr2d2]

There are different terms depending on usage but not on height:

Multi-storey car park
Block of flats
Office block
High-rise

[BobK]

There are different terms depending on usage but not on height:

Multi-storey car park
Block of flats
Office block
High-rise

The second (and, in the absence of any other information, the fourth) are residential. Note that numbering of the floors in multi-storey buildings differs between Br E and Am E: in the US, '1st 2nd 3rd 4th floors' = in the UK 'Ground floor, 1st 2nd 3rd floors'. I don't know what happens in Canada.

b