Have you checked to see if you have red eye reduction set to on? When I first began using a D5100 I experienced a frustrating delay between shots when trying to take portraits of my grandson when using flash. I had a fresh battery, plenty of space on my SD card etc.
I was advised to check to see if the red eye reduction was set to on and it was. The red eye reduction feature fires a series of pre-flashes and therefore prevents you from taking the next shot before it has done its magic.
As soon as I switched off red eye reduction the problem was solved.