Adding any chemical stuff to lower the pH will not work long-term, as I'll explain below. First more critical issue is the cycling.
Letting a tank "run" for 5 weeks or any period without a source of ammonia will not cycle the tank. There is a good article on the initial cycle at the head of this section of the forum, here is a direct link; please read it so you will have a better understanding of the "cycle." http://www.tropicalfishkeeping.com/f...m-cycle-38617/
Once you added fish, the cycle began, as that article will detail. With ammonia or nitrite above .25 the best action is a partial water change of half the tank water, using a good conditioner. Once a day will not hurt the fish--in fact, it will save them. Seachem's Prime is a good conditioner to use at this point because it detoxifies nitrite as well as ammonia, and as far as I know is the only one to do both. But the detoxification works for 24 hours, so a daily check is necessary.
Do NOT add any more fish until the tank is cycled; adding a fish means increasing the ammonia, and until the bacteria that handle the ammonia and nitrite are established, this will only throw off the cycle. You will know the tank is cycled when ammonia and nitrite both are zero for consecutive days.
I would also test your source water (tap water) for ammonia and nitrite; some tap water contains one or both, and this is worth knowing so you can be sure you are dealing solely with conditions in the tank. If there is ammonia or nitrite in your tap water, I can explain how to deal with that later.
Now, back to the pH issue. As your tap water test determined, the pH is 7.6-7.8 in your tap water. pH is connected to the hardness of the water. Hardness is the amount of dissolved mineral, mainly calcium and magnesium, in water. The hardness works to buffer the pH, keeping it where it is. When you add chemicals to lower the pH, they do temporarily, then the hardness buffers bring it back. The resulting fluctuations are far more stressful to fish than simply leaving it alone. So, do not use pH adjusters.
As for naturally and safely lowering the pH, this will depend upon the hardness. You could buy a test kit for hardness, but it is easier and less expensive to find out the hardness from your water supply people. Some have a website, or you can just contact them. We need to know the GH and KH if possible; GH is general hardness, KH is carbonate hardness. The KH is what does the buffering, but it is tied to the GH so knowing either will give us a good indication. Once you have the hardness, we can discuss ways of lowering the pH that will not be counter to the hardness. But without knowing the hardness we would just be stabbing in the dark.