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)
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.