Aspiring photographer looking to graduate to an SLR.

Short answer is yes.

I think the D40 is an excellent choice, and the kit lens is 18-55mm, which is fairly wide angle to reasonable telephoto. Without doing some math, it's a little tricky to know if this is exactly a 4x zoom factor, but it's reasonably close.

I think you will find the SLR is a major, huge and wonderful liberation from some of the features of point and shoot cameras, even advanced ones like the Nikon 5400. They are faster, smarter, easier to adjust, more flexible and can grow with your interest in photography. The D40, and the kit lens, are smallish ... for SLRs; overall you'll find it not quite as portable as the 5400. But I think you'll find the trade-off is well worth it.

(Side note: just had a chat with a friend who used to swear by a camera similar to the 5400 -- he recently moved up to SLR. I had been telling him of the great features of SLRs for a long time and he said he liked how small and portable his camera was. Then he got an SLR and wrote saying "Tom, you were right all along" -- on a recent trip where he traveled with the camera he said he took both, but never once used the non-SLR.)