Is the iphone 5s significantly faster than the 5?

Was wondering if it was worth it, i'm eligible for an upgrade and I can get a 32 gig 5 for the same price as a 16 gig 5s. I really don't care about the camera, I work with students and use my iphone as a quick reference sometimes for homework help… I currently have a 4 and get annoyed at the wait times

Added (1). So would you recommend that I just go with the 5 with more space?

No, there's very little difference in speed between 5 and 5s

IPhone 5 & 5C has an Apple A6 processor,
iPhone 5S has an Apple A7 processor, which is twice the speed.

Yes, its dramatically faster and better battery life too.