Well, there are basically two ways you can get stronger --- higher civ levels and better spell gems. New abilities all come from crafted items, not levels, however; levels just make you tougher and more dangerous, allowing you to enter higher-level regions. So to get more abilities, you mostly want to craft new spell gems, although there are some cool things like bear traps and turning into a bat you can get from turning spell dust in scrolls.
To get new spells, you need the six basic gems and other crafting materials. Gems are all found in caves, mostly behind bat bosses, while crafting materials come from surface areas and caves, either from trees or veins of rock or metal. Trees are very common, while veins are rarer, but marked on the map with a bright green dot.
At level 5, you aren't ready to start entering level 10 regions to get tier II spell gems, but you can explore caves (if you haven't found them, you can look on the minimap for chunks called "surface with caves" for entrances, then head toward red and yellow rooms on the minimap for bosses and gems) to get more tier I spell gems and craft some new spells that cost a bit more to use but have more bang than your basic fireball. Personally, I find lightning ball and energy burst to be especially satisfying higher-cost spells, but I think people are also very fond of things like death touch and tidal (wave? burst?---I forget). Ice cross is fun if you can use it well.
Of course, to get these spells, you'll need new secondary crafting materials as well as spell gems. If you go into the spellgem bench, it shows all the gems and material combinations, even if you don't have them, and you can check out what you might be able to make and hover the mouse over the component to get a tooltip suggesting where you can look for what you want.
Of course, in addition to pimping out your spell bar, you'll also need experience. It seems like you basically get how this works --- ordinary monsters are worthless for exp, only microbosses+ count --- and of course the higher the level, the more they're worth. So if you want to level up, you should definitely be in regions of your level or one or two higher (past that it gets pretty damn tough). Caves, rare commodity towers, and if you can find them at your level evil outposts are great places to find a lot of bosses close together. Rare commodity towers are bit more fun than caves for the time being, since caves only have one type of boss so far, but caves have better rewards --- so far, you can only get one combat spell from a tower, which is admittedly the impressive throw meteor. I think five-six decent boss fights at your own level should be enough to level at the lower levels.
Hope this helps!