As I understand the 5-Foot Step, it can be taken to move 1 Square while still being able to perform a Full Attack without evoking an Attack of Opportunity. Does this mean that I can still Tumble in order to get the benefit from Acrobatic Strike? Or does the Tumble HAVE to avoid an Attack of Opportunity in order to get the bonus?
You cannot Tumble during your 5 foot step.
From the SRD on 5 foot steps:
From the SRD on Tumble:
So, Tumble requires normal movement, and a 5 foot step is only available if you didn't move any actual distance in the round.
Acrobatic Strike is a poorly written feat that does not make any sense.
It requires that you Tumble to avoid an Attack of Opportunity, and gives you a bonus against the foe who otherwise would have made an Attack of Opportunity.
The problem with this is that you do not get to make a Tumble check when an opponent announces his intent to make an Attack of Opportunity; you have to do it before you move. And once you’ve done so, you do not provoke at all, and no one is making any Attacks of Opportunity. The wording of Acrobatic Strike states that you only get the bonus against an opponent from whom you’ve avoided an Attack of Opportunity, but if you never provoked he never got the option to choose whether or not to make one in the first place.
And fixes like assuming that you get the bonus against anyone who you would have provoked from had you not made the check are also awkward. What if a character had Reach you were unaware of, and you would have provoked an Attack of Opportunity but had not realized it? What if you would have provoked, but the target had no Attacks of Opportunity remaining? Or if you’d observed him having made one Attack of Opportunity, but he has Combat Reflexes?
Overall, the feat is poorly designed, and ultimately the effect, however you rule it, is fairly weak. I recommend just not bothering with it at all.
But you can Tumble on a 5-ft. Step, as it is movement, and as long as you hit DC 15 (unless you take a −10 penalty to move at full speed, though, you don’t actually go anywhere), you avoid Attacks of Opportunity. Not that 5-ft. Steps provoke anyway, but that does not seem relevant; Tumble doesn’t have any restriction of that sort, nor does Acrobatic Strike.