It helps, but it depends on your eyesight.
Ona 17" laptop screen with 1920x1080, it is small when trying to setup to run multiple characters and have them all visible. But it works, and you don't have to move the mouse too far. When I was younger I managed to play games on a 14" TV so I probably shouldn't complain too much.
It's really a numbers game. A larger screen in physical dimensions makes it easier to see what is going on. A higher resolution screen makes everything look nicer. I would say the minimum you should be looking at would be around 20" @ 1920x1080. If you get higher resolution, try and increase the physical dimensions too. A 27" @ 2560x1440 is a good spot. 40" @ 4k (3840x2160) is good (physically smaller and it will make everything teeny tiny to look at, despite looking nice while it does it).
As for the computer. The specifications noted above are for 1 copy of the game. Requirements for multiboxing aren't linear, and can get tricky to guestimate in certain circumstances, but for 5, it should be reasonably easy.
You probably should be looking for a computer with at least the following for a good m/b experience:
- intel i7 6700k
- 16GB RAM
- 250GB SSD
- Nvidia 970 or better
Like anything, the above is subjective, other will disagree, and you obviously would need a bunch of other things in order to actually put a computer together. I think, to actually enjoy multiboxing, without having to compromise too much on the graphics, or spending ages trying to tweak to the hilt to eek out every clock tick, then the above would be a good starting point.
All depends on budgets really as they are always the biggest influence over what you get. If you have a budget in mind, and what that needs to cover (currency helps too), then it is always good to look through
www.pcpartpicker.com and add in what you think you need to the price you're willing to pay. You can then link that, or post spec here and ppl will help out with recommendations if they're needed.