Yes, You Can
On its turn a typical creature can take a standard action (e.g. a standard attack) and a 5-ft. step and an action that counts as a move action (i.e. a move-equivalent action; e.g. retrieve an item)--or, if the creature wants to, it can instead take that identical set of actions in a different combination.
The restriction on taking a 5-ft. step is that the creature can't have taken any other actual movement.
"What's Movement, Exactly?"
The section Move reads
The simplest move action is moving your speed. If you take this kind of move action during your turn, you can't also take a 5-foot step.
Many nonstandard modes of movement are covered under this category, including climbing (up to one-quarter of your speed) and swimming (up to one-quarter of your speed).
The section Tactical Movement reads
Your speed is determined by your race and your armor (see Table: Tactical Speed). Your speed while unarmored is your base land speed.
The Move and Tactical Movement sections' silence on abilities that take the creature from its location to another via a means other than its Speed strongly implies that the game considers movement something a creature does with its Speed instead of, for example, a function of the creature's final location on the map.
The section Take 5-Foot Step reads
You can move 5 feet in any round when you don't perform any other kind of movement. [...] You can't take more than one 5-foot step in a round, and you can't take a 5-foot step in the same round that you move any distance.
While the DM can rule that a creature is incapable of taking a 5-ft. step before or after using an effect that transports the creature from his space to another via a means other than his Speed (e.g. the spell dimension door), such a ruling has the section Take a 5-Foot Step overriding the other sections describing movement.