No - firstly, they require completely different living conditions - and secondly, alligator lizards are carnivores - and would eat the gecko !
Gecko
No lizard can live in a 5 gallon enclosure. 10 gallons is the minimum for any lizard and there are plenty that can live in a 10 gallon 1) One Leopard Gecko 2) One Green Anole 3) One Brown Anole 4) One House Gecko 5) One Collared Lizard 6) One Fence Lizard 7) One Alligator Lizard ---These animals can live in a ten gallon BUT that is minimum and they should have a 20 gallon for maximum happiness but they live fine in a ten. The anoles are small enough that you should be able to have one happy happy lizard in a ten gallon ------Please do research before buying any lizard as a pet. They require for specific items. Special lighting, temperatures, humidity, food et.
An alligator lizard is any of various species of lizards in either of the genera Elgaria and Gerrhonotus.
Common house lizard is Gecko .
Starts with an A and ends with a LLIGATOR.
Gecko
Assuming you mean gecko, its a lizard. Google them, there is the Leopard Gecko, Crested Gecko, and the Gargoyle Gecko, just to get you started
a gecko is a lizard and a rattle snake is a snake.
Gecko and alligator are different species. It's as impossible as a parakeet turning into an ostrich, or a kitten growing into a lion.
Yes only a few the 5 lined skink, western skink ,northern alligator lizard and the short horned lizard.
Gecko
It's probably not a good idea. Alligator lizards tend to feed on other lizards that are close to or greater than their own size.