Is it cheaper to bot on a VPS ($4.99 p/m) or on my own PC running 24/7?

Depends.

I would personally run it on a VPS. 

I heard most VPS companies run their servers using the same IP. Wouldn't Jagex notice this?

$4.99 a month for VPS is very good rate, just letting you know (a little off topic) but be careful when using VPS's. Never use a VPS that is made for botting, most botting VPS's are known to access the VPS and steal your accounts stuff, leading to people blaming it on osbot. But using a VPS that is meant for normal stuff and not botting, they aren't going to hack you considering they probably don't know what runescape is.

Thanks, I've already taken this into consideration.

if you can run on your computer and it doesnt stop you from other activities on it no reason to buy a vps

get vps if you got good internet connection only.

get vps if you got good internet connection only.

No.

What are the specs of the $5 VPS?

$4.99 a month for VPS is very good rate, just letting you know (a little off topic) but be careful when using VPS's. Never use a VPS that is made for botting, most botting VPS's are known to access the VPS and steal your accounts stuff, leading to people blaming it on osbot. But using a VPS that is meant for normal stuff and not botting, they aren't going to hack you considering they probably don't know what runescape is.

Actually VPSs made for botting are more suitable as the host has specific hardware and knows what to do, for like the CPU usage, how much CPU and the memory the bot will use all this is in consideration so the host dosent suspend your vps.