Do I need soffit vents when I have 2 gable vents and 5 normal peak vents?
In a nutshell, yes, soffit vents prevent moisture from doing bad things to your home. Greebo is spot on, you want soffit vents for your air intake.

Without a continuous flow of outside air, the attic heat in the winter will melt ice and snow at the top of the roof, which will flow down and refreeze when it reaches the cooler bottom of the roof. This forms an ice dam, backing water up into your shingles and roof, resulting in some potentially expensive damage.

You also want to draw air in from the soffits which are on the underside of the roof and exhaust it at the top, which requires at least the same, if not more soffit vent area than you have ridge/gable vents. This prevents wind blown moisture from being driven up into a ridge vent and into your attic. If there is a positive flow of air out the ridge vent from the soffits, this minimizes the risk of the ridge vent becoming an intake vent.

And finally any moisture that does accumulate in your attic will be quickly vented away by the airflow from the soffit to the ridge vents. This includes any moisture from the outside reaching the dew point and from any moisture from your home that escapes into your attic from any cracks.