Download and run GPU-Z and see what specific HD5xxx GPU Card you have installed. At the upper right corner where it says "Look Up" click on that and it should show the specs and resolutions at TechPowerUp website.
Here is an example of a HD5850 Mobility CPU from TechPowerUP: ATI Mobility Radeon HD 5850 Specs | TechPowerUp GPU Database
This for the HD5145 Mobile specs:
So once you know exactly which HD 5xxx you have installed you can look it up at TechPowerUp website to find out what resolutions it supports.