That's not a bad set of parameters (except for the nitrates). I have about the same water, and my betta is fine.
A lot of the test kits' literature make you feel like your pH, GH and KH need to be at certain levels, which really isn't true for most fish. Your LFS will be selling fish from basically the same water, and they don't usually alter their water.
As long as you have no fish in there, you can "test" your cycle by adding the same amount of ammonia you added to get it to 5ppm, wait 24 hours, and it should be 0 again if your cycle bacteria are still there. You can do a 99% water change to get your nitrates under control, or do daily water changes. The bacteria aren't generally in the water, but on the hard surfaces and in your filter media.