6 skills (1st tab) - 6 abilities, 3 per tab (2nd tab)
In the Hero tab: 1 slot for a racial skill (level 3) + 3 slots for racial abilities + 1 slot for a global skill. In total, that's 5 slots, as shown in your picture.
Overall, the situation is workable; I think this version is close to perfect. It's better than the initial version created by the game developers.