You can statically assign each computer an IP address or have DHCP dynamically lease addresses. To logically separate these 5 different parts, the best way to do this would be to break down your class C network into smaller subnets. Here's an example:
Let's assume 192.168.1.0/24 is your Class C. Let's also assume you want this to be 5 separate but equal networks. A class C network is broken out like this: 192.168.1.1 - 192.168.1.255. .0 is your network address and .255 is your broadcast address. These are not usable as host addresses. So let's break this down into 5 separate but equal networks:
192.168.1.0/27
192.168.1.32/27
192.168.1.64/27
192.168.1.96/27
192.168.1.128/25 <--- You can leave the second half of the class C intact as a larger network, or you can break it down into 4 /27s if you wanted. Use the following link as a cheat sheet:
https://www.aelius.com/njh/subnet_sheet.html
Now, as far as making these logically separate, you would need to designate these separate networks as VLANs. This can get complicated as we're creeping into network infrastructure territory with all sorts of different variables like firewalls, ACLs, whether or not you want inter-VLAN communication, etc. But that's a different discussion so we won't get into that.