Yagi's are designed for specific narrow band frequencies. It will always work best at the design frequency.
They are technically end-fire traveling wave antennas with some fairly critical dimensions.
Summary - best used at design frequency and it will probably degrade signal at any other.The reason they picked 5.8 is because the dimensions are small enough for mounting directly. The dimensions would have to be roughly doubled for 2.4 Ghz. Unfortunately 5.8 being a shorter wave attenuates faster (trees etc) and has less reflectivity (nearby buildings and such). But then there's usually less interference.
My favorite is still a BiQuad antenna which you can build yourself