How to display a big background in your game
Really big images can reduce the performance of a game, as they are costly to transfer and store in the graphics card memory. They are also weighting more in your game package, making the download and loading longer for players.
As possible, try to stick to smaller images. Avoid anything larger than 1024x1024 or 2048x2048. If possible, repeat the image, using a Tiled Sprite object. Tiled Sprite can be as large as necessary without any impact on performances.
If you still want to display a very large, high resolution image, it's in this case a good idea to split it into multiple, smaller images, and display an object for every image. You can also use a Sprite, and have a different image in each animation. Then, put multiple instances of the object on the scene and change the animation of each instance to recompose the original image.