Can we say: "This room is about 5 by 8 meters wide"?

I don't really see anything wrong with it. You should understand though that it is short for:

"This room is about 5 (meters long) by 8 meters wide"?

"Wide" is one dimension.

It's important that you asked "Can we say..." because I believe there is more leniency in speech than in writing. I wouldn't write it.