Using prime lenses indirectly make you think a lot more about composition. This is fantastic to learn and find a style, yet comes with challenges. My favorite setup is a 50mm f1.4 and a 5D (which would have a comparable FOV to the 35mm on the D5100)
Using only primes for event photography. I will never forget one of my first paid events.
I tend to have a facebook oriented distribution, and from a meeting with the clients, all I really had been hired to do was get people new profile pictures! Profiles and half body crops were all I was aiming to shoot.
All I took to the event was a 50mm on the old 5D mark i and a flash. When the guests started arriving one girl was adement that I should get a full portrait of her and her friend. I took a few paces back and with my back against the wall and I still couldn't fit them both in. We had to march through to a larger space in poor lighting and try again there.
Using a prime means you have to move around to get the composition how you want it. This is rarely convenient. Even taking several primes is a faff. My new setup at events involves two cameras, one with a standard prime, the other with a zoom.
Street photography. Although stressful in a professional context, going and doing street photography without a zoom function is very liberating. You have to often get yourself right in the heart of the scene to get the shot (unless you're using some 500m Tamron jobby!).
Numbers aren't everything. Consider both lenses before you spend wads of cash. I think you should try out the lenses for a couple of days and then buy which ever you prefer using. No other answers cover this aspect of fixed length lenses. The internet is already bloated with people praising the prime lenses for the optic quality and faster apertures.
I run a photographic society and we have a community thats friendly enough to share lenses. A member recently purchased a Canon with the kit lens and a 60-200mm zoom lens. Dissatisfied with his choice, I lent him the canon plastastic 50mm and within a few days he sold the zoom tele photo lens and bought a 50mm prime. All the members who have tried primes, go out and buy them. They do tend to just stay attached to your camera.