Is it this what you have Ron? Plus, what is the frame rate your shooting at?
That's the same camera, but that lens is a 100-400mm. I have a 400mm 5.6 L prime lens ( Fixed focal length no zoom )
Not sure about frame rate. I keep it set on the one where you hold the button shutter button down, and it shoots repeatedly as fast as it can. Here's the image info for one of the flying shots. I see I had a shutter speed of 1/800. Surprised it caught the flying bird at all. Usually need a shutter speed twice that fast for flying birds. Another reason I got this camera is it works great with High ISO for low light conditions such as this.( Low noise at high ISO )
File Name 054.CR2
Camera Model Canon EOS 5D Mark III
Firmware Firmware Version 1.1.3
Shooting Date/Time 2/22/2016 1:50:09 PM
Owner's Name
Shooting Mode Manual Exposure
Tv( Shutter Speed ) 1/800
Av( Aperture Value ) 6.3
Metering Mode Evaluative Metering
ISO Speed 1250
Auto ISO Speed OFF
Lens EF400mm f/5.6L USM
Focal Length 400.0mm
Image Size 5760x3840
Image Quality RAW
Flash Off
FE lock OFF
White Balance Mode Auto
AF Mode AI Servo AF
AF Configuration Tool Case 6
Tracking sensitivity 2
Accel./decel. tracking 1
AF point auto switching 1
AF area select mode Spot AF
Picture Style Landscape
Sharpness 4
Contrast 0
Saturation 0
Color tone 0
Color Space sRGB
Long exposure noise reduction Disable
High ISO speed noise reduction Standard
Highlight tone priority Disable
Auto Lighting Optimizer Disable
Peripheral illumination correction Enable
Chromatic aberration correction Enable
Dust Delete Data No
File Size 28559KB
Drive Mode High-speed continuous shooting