Installing 5 frost free stand pipes

Is there a way I can install 5 frost free stand pipes in a row (each is set up on a livestock pen) where I can have all 5 running water at the same time? What size of main water supply line would I need?

Anything is possible in plumbing....
Often it just comes down to a question of cubic Dollars...
How many boxes full of money do you have?

Seriously how are you planning to supply all of these at once?
Well or municipal water supply?
It's probably going to be your limiting factor.

I am on a municipal water system.. I have tried to use the standard 1" poly pipe but when I turn more than one or two faucets on everythings slows down, the third and fourth won't run until I have shut off the first 2.

I am on a municipal water system.. I have tried to use the standard 1" poly pipe but when I turn more than one or two faucets on everythings slows down, the third and fourth won't run until I have shut off the first 2.

Well thats the good news! You have an unlimited supply!
Now all you have to do is find a way to get it to where you want to use it.
As you already know a 1" pipe isn't going to do it. I would start with checking with your water company to see how much you service and meter can do. If that is capable then the calculations will have to be made to see how big of a line you need run.

Depending on what size hydrant your installing
1/2" pipe you can get 6gpm
3/4" pipe you can get 11gpm
for five units it would be 30gpm or 55gpm

1-1/4" poly pipe will get 32gpm
1-1/2" poly pipe will get 44gpm
2" poly pipe will get 70gpm

This is the maximum gpm pipe will supply, it does not have to be the total volume out of each hydrant you don't need it to come out full blast for drinking.
More important is you need to pipe them in a group and not one after the other as the first will get the most and the last the least. It's like body sprays in a shower.

And then you have the factors of distance and elevation.