Paper jam issues in HP Deskjet GT 5820 is quite common and can be occurred as real or false. Sometimes the printer shows a paper jam issue while there is no real paper jammed. However, sometimes actual paper gets jammed and you find it unable to take prints. Below are the steps to solve this issue:

1. Try to find the jammed paper
2. Check if carriage can move freely
3. Make sure paper rollers are clean
4. Ink smears should also be cleaned
5. You can clean paper rollers manually inside the input tray area
6. Now reset your printer

These steps are verified and can easily solve your issue but if you need a detailed solution you can call at HP printer customer service and get your issues fixed easily.