How many computers can a family run on one wireless router and not have problems? If the family has 5 computers running at any given time all at once, what is the consideration in purchasing a wireless router?
As far as absolute max, see here for some examples. The lowest models support 32 clients, which seems reasonable. This is probably just the maximum number that the router can talk to due to hardware and software limits. So 5 computers will not be an issue.
If you are concerned about performance, that is a different matter. If people are just browsing the Internet, there should be no problems. You will probably be limited by Internet speed before you have router issues.
If you are copying a bunch of files between computers often, then it gets complicated. In that case, a general idea would be "more antennas." Having more antennas can help the router talk to more devices at the same time.