Your problem might have something to do with how you have your bios setup or the bios version you are using does not correctly support this CPU. The CPU-Z program is showing a maximum multiplier of 22 which is a sign that the bios is not setting your CPU up correctly. Go to the Gigabyte website and make sure you are using the latest bios version for your motherboard. Before you boot up, go into the bios and make sure SpeedStep and Intel Turbo Boost are enabled. The default turbo ratio limits for the Core i5-6500 are 36, 35, 34, 33 when 1, 2, 3 or 4 cores are active. This has to be set correctly in the bios.
If you cannot get this problem fixed in your bios, I would try using ThrottleStop. It lets you adjust the maximum multiplier as well as the turbo ratio limits, enable turbo boost, etc. Post some screenshots of ThrottleStop if you need help setting this program up. The latest version is available at TechPowerUp.