Yes, or get a smaller carboy! Either way is fine.
You can generally "top up" with a little water or already made mead if you have a tiny bit of headspace to fill, and some folks use sanitized marbles to raise the level of the mead or wine a bit- but for over a gallon, you'd need an awful lot of marbles.
Generally, the carboys hold a bit more than exactly 5 gallons anyway, so commonly if you want to fill a 5 gallon carboy, you'd make 5.5 gallons of mead. I do that with wine all the time, as each time you rack you'll "lose" a bit of wine or mead. So make extra, and keep it in wine bottles or a growler or a gallon jug or something with a bung and airlock, and use that for topping up. You can always top up with a similar finished mead, so you don't water down the batch, but if it's your first batch of course that won't work.
For wine, I sometimes will use a similar commercial wine if I don't have a homemade one to use. For example, I may use pinot grigio to top up a dandelion wine or mead. But that's only in small amounts, like a cup or two, and not gallons.