For reference, here is the downloadable NFL rulebook, and the particular section that applies to this is Rule 14, Section 1, Article 2, Item 4:
Ball in Advance of Line to Gain: If the ball is in advance of the line to gain after the enforcement of a distance penalty for a foul by team A during a play of scrimmage, it is first-and-10 for Team A.
So it is possible to get a first down with an offensive penalty but it depends on the where the ball ends up after enforcement of the penalty.
Basically, a holding penalty (a live ball foul) of 10 yards is marked off (1)from the line of scrimmage if the foul occurred behind the line of scrimmage, (2) from the spot of the foul if it's committed past the line of scrimmage but behind the downed spot of the ball, or (3) from the downed spot of the ball if it's committed ahead of the final downed spot. For the example you give, I think you're most interested in #3--even if the hold occurs further down the field, say the 45 yard line, the penalty will be marked back from the end of the run (from the 35 to the 25).
Since this is a live ball foul, it's essentially part of the play and any new down can't be determined until marking off the foul (if the defense accepts the penalty). So the fact that the runner reached the first down marker doesn't matter; what matters is the spot of the ball after marking the penalty. In that case, the end result of your scenario is that it would be 2nd and 5. Basically, you can't separate the result of the play and the penalty into two different things; that's the definition of a dead ball foul of which holding is not.
To answer your main question, there is one way to gain a first down on a play where the offense is flagged for holding, and that would be to have both the downed spot of the ball and the spot of the penalty more than 10 yards past the first down marker. After marking off the 10 yards, you clearly can't have a "2nd and negative 4", for instance, and the above stated rule is applied so a first down must be rewarded.