Yes, there would be 5 channels used. But I still recommend getting the Futaba 7ch as a minimum entry functionality-wise.
Have you picked out a gyro to use yet? Some require an additional receiver channel. I know that the Futaba gy401 head hold gyro does, and this is the most commonly recommended gyro for helis in the class your have purchased.
Oh, and I mistypes the link above
brucknerhobbies.com
$169 for the 7CH transmitter only.