How can I construct my own capacitor?
You need to do some basic calculations first. The formula for capacitance is

$$C = \epsilon_R \epsilon_0 \frac{A}{d}$$

Let's say you want to use 1-mil (25.4 &micro;m) waxed paper as a dielectric Note that this will determine the voltage rating of your capacitor. The dielectric strength of waxed paper is about 35-40 MV/m, so this will give you a capacitor that can theoretically handle almost a kilovolt, but be conservative in how you use it!

The relative permittivity of waxed paper is about 3.7, the permittivity of free space is 8.854e-12 F/m. Solve for the area required:

$$A = \frac{C \cdot d}{\epsilon_R \epsilon_0}$$

$$A = \frac{5 \mu F \cdot 25.4 \cdot \mu m}{3.7 \cdot 8.854 \cdot 10^{-12} F/m} = 3.8767 m^2$$

If you get aluminum foil and waxed paper that's about 12" (30 cm) wide, you can probably get an overlap of, say, 25 cm, which means that you'll need a length of about 15.5 m to get the area you need.

If you then roll up your capacitor (using a second layer of waxed paper), the capacitance will be doubled, or about 10 &micro;F. Obviously, this will be physically rather large, over a foot long and several inches in diameter.