I'm absurdly new on networking, and I just want to know if it possible to set a network with 3 computers without a router, switch; just UTP CAT5 cables (or any category)
It's theoretically possible if one of the computers has two network interfaces. Otherwise, how would you connect them all? But that would be a kludge at best.
If you are actually thinking about doing this, don't bother. Network switches are very cheap.
Well you could get old school and use 10Base2 if you find the proper networking cards for your computers. You just need some RG58 cables, some T connectors and two terminators.
Assuming you are talking about Ethernet:
Ethernet was originally based on the idea of computers communicating over a shared coaxial cable acting as a broadcast transmission medium.
In a modern Ethernet, the stations do not all share one channel through a shared cable or a simple repeater hub; instead, each station communicates with a switch, which in turn forwards that traffic to the destination station.
Practically speaking, you don't need any cables at all. WiFi (wireless LAN) technology is dirt cheap and has reached LAN speed/performance. Every laptop, tablet, and smartphone ships with a WiFi network interface card, NIC. Many PC's ship with them, or can have one plugged in.
All you need is a WiFi access point, sometimes called a WiFi router.