The Mini-Breakout Board has an internal voltage regulator that allows you to power the board with a power supply in the range of 7-15V. I've checked the following site: SparkFun Block for Intel® Edison - Base - DEV-13045 - SparkFun Electronics, and the SparkFun* base block only has two micro USB ports. One port is used to access the terminal, and the other one is the USB OTG port. I've checked the schematic (https://cdn.sparkfun.com/datasheets/Dev/Edison/Base_Block.pdf) and the only way to provide power is through the USB ports, so powering it with 5V seems to be fine.
Anyhow, if you want to know more details about the SparkFun* base block, I recommend you to check its description directly in the SparkFun* site: SparkFun Block for Intel® Edison - Base - DEV-13045 - SparkFun Electronics
Update: I tested it out and the sparkfun base block can support a camera and microphone using a 5V/1A supply.