Skydome is not a solution, it requires huge textures. You must find other ways.
Remember Hollywood, you only put in scene what you see.
For background you can use only a plane covering what the camera see. With animations becomes more tricky, depend on how much need to change the background with different frames you will need a bigger plane. You can tile the plane, will a good tilling nobody will notice in the moving scene that the background is repetitive (video games).
You can do more tricks. In a frame you see the landscape and a background image, then in the next frames you point the camera to see only the terrain and in next frames you see again the landscape with background, but this time the background plane was rotated and has other texture image.
If you want you can use a skyglobe for global illumination for the scene, but this time the texture is a low resolution and blurred,  you needn't detail for illumination and you do not see the skyglobe, it only illuminate the scene.

Stupidity also evolves!