After five years of dating the same person, both peoples' fallibility is clearly established. There's no benefit to hoping to maintain an aura of perfection by never admitting you're wrong. It's juvenile to think that you shouldn't apologize for errors. By apologizing, you're showing maturity, and you're also demonstrating that you have the balls to risk her potential rejection of your apology.
If you really were ****ing some other girl, then you might as well not apologize since you were just telling the truth.
edit: Send her something more personal than flowers. Perhaps you could make something and incorporate a picture of the two of you into it as a visual reminder to her that you two are right for each other.