I can understand the desire to squeeze a little more distance out of the 3wt. I love fishing my 3wts, and though they're often most used on smaller water, I know that I have had times when I've needed to throw longer casts to rising fish or to nymph a far seam. The 3wt is going to appear at first as a huge change from the 5wt. Since you're not only dealing with a change in action/flex but a change in wt, as Davo said, you're going to have change up your casting stroke speed a bit to match the rod. While feeling the rod may help you find the cast, in my short tenure as a fly-caster I've also had success pairing the feel with watching the line straighten out behind me to time my cast. As Fred said, you will likely be better off with a weight-forward line rather than a DT. On top of that, I was told that the Allen lines tend to be a half a line weight lighter (never weighed them myself, but had the inclination when casting on a matching rod and attempting to go for longer distances). While you can certainly cast a lighter line just fine once you get the action sorted out, you would likely be better off with a definite 3wt WF line, and put the extra money into getting a better line. The higher-end lines do legitimately get you more distance and it tends to feel better casting them. If you're on a budget, see if Orvis still has any of their Wonderlines on clearance, since they released their new line series they've been clearing out their previous line series. If they still have them, you'll get a heck of a deal.
Most importantly, good luck! I'm sure you'll get it ironed out and get to throwing those longer ropes soon enough