I've never gone by the book as far as diet, but it was my understanding that the book's diet was not in a deficit, but a small surplus. When eating at a surplus you will gain both muscle and fat while adjusting your overall bf%. how are your clothes fitting? Re-read the section about diet and verify discussions regarding eating at a surplus or a deficit.

So I gained 5 pounds in 3 weeks, which was 2.81 pounds of fat and 2.19 pounds of muscle.

Is that possible in only three weeks?

I am pretty sure that is mathematically and biologically impossible. Someone correct me if I have my numbers wrong, but if it takes a surplus of 3500 calories to gain 1 lb, that's 17500 too many calories you've been eating over those three weeks. I doubt that you've done that. Plus, I don't think your body can add muscle OR fat that quickly.

I do not think your body fat anlysis tool is accurate. They say calipers is the only accurate method (excepting water immersion or whatever it's called... body fat baptism perhaps?)

Especially since you don't notice a difference in how your clothes fit, I'd say keep doing what you're doing and don't stress out about your weight or body fat so soon after starting the program. As allabtlm said, you are eating at a surplus, however it's necessary to do that if you want to gain muscle. If you love the program and lifting heavy, and you're enjoying the change in appearance, I'd say keep doing what you're doing.

But if you're not feeling patient, and you really want to lose weight faster, you may want to do a cut before starting this program. Quit working out, or keep your lifting even to keep the strength you've gained, and eat at a deficit for a few months to lose some weight. THEN go back on NROL and be sure to eat at a surplus again to gain muscle. Similarly you could finish the program and THEN go on a cut. http://scoobysworkshop.com/ has some good info about cuts; however he does seem to think women should lift differently than men... just ignore that nonsense

I can guarantee that most of your additional weight is water weight. Not fat or muscle. The Omron hand held device is great for a guideline, but it's not perfect by any means. Have you ever done the measurement more than once within a few minutes? I have and I've gotten results that vary almost 2% at times. Women are not physically capable of putting on more than .25 lbs of muscle a week, which means you would have to be eating at a surplus for over 2 months to gain that much muscle. It's very easy to fluctuate 5lbs of water weight, especially when lifting or starting a new exercise program. Give it a month and see where you are then.