It sounds like your computer is heating up too much. I've noticed that Macs will often wait until they are far too hot before turning the fans up.
It sounds like you start Minecraft, and your computer is cool, then, your computer heats up over a period of five minutes, and starts to go slowly.
Then, your computer turns its fans up, and cools back down to an acceptable level, enabling it to run quickly again.
I recommend using smcFanControl. It will display your computer's current temperature, and fan speed, and also allow you to manually force your computer to use its highest fan settings. If you enable the high fan speed before starting Minecraft, then hopefully it won't heat up as much.
You can also try reducing the load the Minecraft is putting on your system.
In my case, I found that using 64 bit Java caused Minecraft to run faster, and at a lower temperature.
I also enable Advanced OpenGL, and reduce the graphics to something slightly less than maximum.