Read the section on astable operation, in particular the bit about choosing R1, R2, and C1 (referring to their schematic, not to yours). You can replace R2 with a variable resistor.
From what I can tell the circuit would work, however it is not necessarry to drive each LED individually via a transistor. I would drive a couple LED’s from each transistor. Don’t forget the correct resistance for the transistor to avoid pulling too much current.
Be careful. In the diagram above, you now have the current for all five LEDs flowing through one current limiting resistor. You have to adjust the value of the resistor.
Let’s say you want each LED to run at 25mA. So your target current through the resistor and transistor is:
5 x 0.025 = 0.125A (125mA)
Let’s say the voltage drop through the transistor from collector to emitter is 0.6V, and we’ll stick with 1.8V drop for the LEDs (You need to look up the actual voltage drop for your LEDs.) To determine the voltage drop across the resistor, we subtract these two numbers from the supply voltage:
5 - 0.6 - 1.8 = 2.6V
To determine the correct value of the resistor, use Ohm’s Law (V = IR), solving for R:
R = V / I = 2.6V / 0.125A = 20.8 Ohms.
Be sure that your resistor can handle the current. I’d go with a 1/2 Watt resistor to be safe.
BTW, you won’t find a 20.8 Ohm resistor. Just use the closest value you can find. You can re-run the calucations above to be sure you know what current to actually expect.