My new Apple Watch 5 is not charging

If you got it less than 14 days ago and from an Apple store, you can return it no questions asked for a full refund. Bring all of the accessories and the watch. If you did not get it at an Apple Store, you are going to have to find out their return policies. If it wasn’t Apple and you have troubles returning it, then make a Genius Bar appointment at the nearest Apple Store to have the device examined by Apple. They will explain your options from there.

Did you remove the plastic around the back of the Watch? Did you check the plastic around the charging puck? See this for other suggestions, If your Apple Watch won't charge or it won't turn on - Apple Support