Can my iphone and apple watch series 5 have different cell carriers

No, they need to be on the same plan.

They should be on the same carrier and on the same account, but they don't have to.

If the two devices are on two different carriers, the watch will generally be limited to behaving as if it is a GPS-only version of the watch. In such case, as a rule, they will need to be within Bluetooth range of each other for many features of the watch to work, since you would not have the carrier's network to facilitate coordination between the watch and its host phone.