How do I know if my series 5 Apple Watch has cellular and I can leave my iPhone at home?

You would have had to specify you wanted the cellular model when you bought it, and you would have had to set it up with your iPhone's carrier to have it connect the cellular network and have the extra monthly fee added to your iPhone's service plan.

Also the model number will tell you if its the cellular model: Identify your Apple Watch - Apple Support

Though you would still need to set it up with your carrier for it to use cell service when away from the paired iPhone.

See here;