Several good suggestions above.
When you shoot high fps, the camera has internal memory that holds or buffers images while they are being written to a memory card. Even a fast memory card is slow by comparison to the speed of the buffer. Once the buffer is full, the camera pauses until there is room in the buffer to begin taking images again.
If you write to both a compact flash card and a SD card, the SD card is typically much slower than a Compact Flash Card, and the camera will be limited to the slowest card.
For the best possible performance, get a very fast 1000X Compact Flash Card (Lexar), and do not enable writing to a SD Card. If you only use a SD card, performance will suffer. The 5D Mark III cannot make use of UHS-1 SD card capabilities, so what you may think is a fast SD card is actually much slower than advertised.