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...