T5 Aquarium Lighting

I wonder if I should have aquarum T5 lamps or T5 lamps ordinary house will be OK in my aquarium?

The answer to this depends on what kind of aquarium you have configured. A single fish tank fresh or sea water would be fine with any type of lighting. In this case, the light is more for you than fish. Many fish do not do well in full light of research before buying.
If you use a planted tank or a reef tank, good lighting is essential. I can not give details on the issue of salt water, as there are many corals and inverts requiring different time different colors and intensities. As for freshwater, a full spectrum (5000-6500 Kelvin), the bulb and at least 2 watts per gallon (more if a small 55-gallon tank). You should be able to use any light for your tank, as it responds to your plans.