Will a telus iPhone 5 work on t mobile?

Yes,It will work.
But you iPhone 5 should be unlocked one.If it's locked by telus network means,you will need to unlock it.
For unlocking you can approach your service provider or else try to buy an unlocking service from any one of the online unlocking service provider like WickedUnlock.com Here you can unlock your iPhone using Remote unlocking method.It's one of the best and safe way to unlock your iPhone without jailbreaking.