That kind of light will not suffice.
And since you have a really small tank, I'd rather do weekly water changes instead of employing several filtration systems. If you want something easier, make a small airdriven skimmer. Keep it simple. Water changes would be enough.
Here's a sample computation:
Suppose you buy one bag of blue treasure salt, which costs around 800 pesos and is good for 50 gallons.
You have a 5 gallon pico minus the water displacement by rocks so approximately you have around 4.5 gallons = approx. 17 liters.
If you are going to do 10% WCs, that would be just around 1.7 liters.
1.7 liters x 4 weeks x 12 months = 81.6 liters. A bag of blue treasure is good for approximately 189 liters.
Let's do more math:
For an 800 peso bag good for 50 gallons, that would equate to only 16 pesos per gallon. RO water from water purifying stations would be around 30php/5gallons so that would be 6 pesos per gallon.
16+6 = 22 pesos
So imagine you would spend approximately 22-50 pesos ONLY per MONTH, depending on the volume of water you will change.
Want another sample?
Let's say you use NSW for your water:
Say a gallon of NSW is around 8-15 pesos... that's the total cost you have to pay bi-weekly.
If you will employ lights and pumps for your ATS, compute the total wattage that you will spend on it monthly, aside from the initial cost.
Think about it.
And BTW, If I were you I would save the money to buy a better light fixture for your future corals and save some more for testkits and other essentials.