I have four new Cisco SG 350 28P PoE switches, but no stacking cables. Can I use CAT5E or CAT6 ethernet cables to accomplish stacking them?
Those switches are not stackable switches. You need the Cisco 350X Series Stackable Managed Switches to be able to stack them.
You can connect your switches together as separate switches, not a stack of switches.
To make sure that we understand each other, a switch stack is where the switches are connected in a way that all the switches in a stack appear to be a single switch, and they are managed as a single switch by the master switch in the stack. This has nothing to do with physically stacking switches (other than the fact that stack cables are short, so you probably need to physically stack stacked switches).
Separate switches can be physically stacked, and connected together. The physical connection can be: Category-5e or Category-6 cable for copper 1 Gbps (1000Base-T) connections, Category-6 (short cable runs) or Category-6a for copper 10 Gbps (10 GBase-T) connections, or the correct fiber for fiber interfaces. The separate switches act as separate switches and are managed separately.