I have the same problem. Neither sync nor import is not working in 5.0.3.
I upgraded from Zotpress 4.5.4 to 5.0.2 and then to 5.0.3. Because of problems with shortcode parameters after the upgrade (style, etc. didn't have any effect), I decided to drop the Zotpress-related database tables. After re-activating the plugin and adding an Zotero account, Zotpress would not create new database tables. Also, the API page on Zotero.org would not indicate any communication with a client.
Therefore, I downgraded to 4.5.4, added my Zotero account and imported the library. Database tables were created and everything worked as before in 4.5.4.
At least in my case, the 5.0.3 scripts cannot create the database tables for Zotpress.
I'm using WP 3.5 and have > 2000 entries in my library.
Thanks for your great plugin!