QuickBooks Error 5502 can be categorized as – QuickBooks data has been uploaded, but failed to connect to the server. Error Code 3005, 5503 are also the same category of errors.

Root Cause of QB Error 5502?
This QuickBooks error occurs because of a problem with Intuit online services or third-party developer application connections to QuickBooks. The data in your QuickBooks company file was uploaded successfully, but an error occurred while downloading the changes made by applications using Intuit online services or third-party developer application connections to QuickBooks.

How to fix the QB Error 5502?
Troubleshooting QuickBooks Error 5502

Note: Please make sure before you perform the specific problem solving steps for the error you are facing, you must ensure Sync Manager is up to date. You can ignore this error, if you don’t use any online application that modifies your data.

Intuit servers may be busy or unavailable at that particular time. You can retry the Sync after sometime.
If the above solution does not resolve the issue or answer your question, you can read discussions and post messages and questions relating to your issue on the Intuit QuickBooks Community site introduced by Intuit or you can connect with the QuickBooks technical support for guidance and error fixation.