Jose is correct. PSX does not care about anything really, but you will need to make a physical connection first. This is what is meant by "switch". What you cannot do, for example, is physically split the wires and connect all five computers in parallel to one Ethernet output of your PSX server. You need something to make that split at the electrical (layer 1) and link (layer 2) levels. You can as well use an Ethernet/IP router, but you won't use most of its features -- unless your PCs get their IP addresses via DHCP from this router.
If you use a WiFi/IP router, the WiFi links replace the Ethernet links, so you still have the same solution, even if you don't see wires. Note that WiFi may not be as reliable as Ethernet, depending on how saturated your radio spectrum is.
A "PSX Router" actually lives at the Application layer. It knows what kind of data it relays and provides services that build on top of that, caching and filtering PSX data for its clients. It thereby relieves PSX from data pressure if a significant amount of clients needs to connect to it. On top, it can shield PSX from slow network links such as internet long-distance links, that would otherwise be able to lock up PSX if they don't sink the data fast enough.
In general you don't need a PSX Router if all computers are on the same local, fast, reliable network.
Hoppie