She does not provoke attacks of opportunity when moving in this way, but any other movement she attempts as part of her move action provokes as normal.
Okay so. It seems that you're getting the fluff (a dimensional rift, 5' of movement, part of a move action) of the dimensional slide ability confused with what the ability says it does in rules text.
A GM might rule as a houserule that due to the fluff text of the ability, if you dimensionally slide from adjacent to an enemy, that enemy gets an AoO on you 'as you walk into the dimensional portal' but that would be a houserule. It is not what the ability says. The ability says the following;
- The ability is activated as part of a move or withdraw action.
- It allows you to move [your character] up to 10' per arcanist level to a location you can see.
- Activating this ability costs you 5' of movement [from your move or withdraw action], subtracting that from the regular movement allotted by the action (but not from the arcanist dimensional slide movement).
- You do not provoke attacks of opportunity when moving via Dimensional Slide, but still provoke a normal for the other, regular movement.
This ability is actually amazingly clear about not provoking AoOs.
Now you may (inferring from the question) be thinking that you somehow need to walk some distance to 'count as' having a move action before you can activate dimensional slide, or that the rules text in AoOs about 'leaving a threatened square' supercedes Dimensional Slide's rules text - it's unclear, as the question is written as if dimensional slide provoking AoOs is self-evident. But to answer those concerns, a move action or withdraw action are declared before any movement is made. The order of events is like so -
Jim: 'I'm taking my move action to move out over here, behind these pillars. One-two-three-four-five-'
The DM: 'Okay so when you leave square three and four these two Bugbears get to Attack of Opportunity you, they get 31 and 40 to hit, does that hit?'
Jim: 'Yep. Damn.'
Jim can declare his move action to move and then activate an immediate action magic item that lets him teleport or anything else he's capable of doing during a move action without actually moving anywhere first. There's no requirement in the rules for him to move a distance to 'count as' taking a move action or anything - a move action is simply a type of action all creatures are allowed to take on their turn, at any time during that turn.
As for AoOs from moving trumping dimensional slide, it is actually the opposite. Specific always trumps general in PF. The general case (movement triggers AoOs) is specifically negated by Dimensional Slide saying it doesn't. Dimensional Slide, is a specific movement case, and the rules on AoOs are general rules, ergo, specific wins.
What is unclear about the ability and would potentially fall into GM fiat territory is whether or not this movement can be taken when a character is unable to move as part of a move action, such as when being Grappled or chained to a wall. Even prone movement would probably be enough (having 5' of move to spend) but RAW is sorta silent about when you can take move actions but are restricted from moving normally and this ability.
But the AoO from using it adjacent to enemies very much is not. It is quite specific about how that works.