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You can't have any more spells at 1 time.
But at Level 15 you'll get a 2nd weapon + 2nd set of skills to set up. So you could have 1 for Healing and another for Dps, for example.
Once you get to level 15, you get a second bar that you can swap between. You can also have a consumable, and swap between a ring of various consumables. You also have a 6th slot for your ultimate ability.
While you can only have 5(10 with two bars) abilities at any one point, there is a mod that allows you to change between different skill bars which you set yourself, using a macro.
Here is said addon:
Wykkyd's Outfitter - Save sets of skills/armour for easy switching between roles/builds.
Wykkyd's Framework - Allows outfitter to work, gives macro features etc.
You need both of those in order for the addon to work.