Stars represent the quality and comfort of your inn in the eyes of your visitors. To increase stars you have to buy and upgrade new items and unlock new rooms. To have 5 stars you have to construct all of the rooms and services, buy and upgrade all items in all of them.

To check what you are missing in your Inn to get 5 stars you’ll need to press the management button (bottom right corner of the screen) and select the statistics tab. There, you will see a scrollable list of your rooms and services and a round progress bar for each of them, indicating the progress of your upgrades inside of them. Probably you’ve missed a parking upgrade or something minor :)

Please note: the premium upgrades (that cost gems) are not needed to reach 5 stars.