My first question is are you planning on having a betta in the 5 gallon? Because you've posted in the betta forum instead of FW general issues or filtration and water quality. Just wondering, no big deal. 
Anyways, I have a link for you below on the cycling process and what happens at a bacterial level. Should be fairly easy to understand for most. You are approximately half way through the cycling process. Your ammonia isn't really high (high enough to cause fish problems, but not astronomical). Has your ammonia been reading higher before? First the ammonia spikes, then should be 0 and then you would have a spike in nitrites. The nitrate levels in your tank are currently perfect. Each tank's cycling process may take different times. For example, one tank may cycle in 6 weeks others may take longer than 8. It depends on various factors. Size of the tank and how many fish you added are major factors.
You will have spikes in all (ammonia, nitrite and nitrate). It is a process of getting all the helpful bacteria in your tank to be able to remove harmful chemicals so your fish don't die. If you have any questions after reading the article below, please feel free to ask. I'd be glad to help.
Setting up a new tank
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Phishie
Site Coordinator
"An ounce of prevention is worth a pound of cure."
