Your zipped datasheet is not a valid zip file so I could not open it. Attach it as the original PDF file.
I found a datasheet for the old 2N2222 from Central Semi and it shows a max saturation loss of 0.4V when its collector current is 150mA and its base current is 15mA. Then its base-emitter voltage has a max of 1.3V.
So a 5V supply and the transistor saturating with a loss of 0.4V results in 4.6V across the 30 ohm collector resistor so the current is 153mA.
The 260 ohm base resistor has 3.7V across it so its current is 14.2mA which is pretty close to the recommended 15.3mA. 260 ohms is not a 5% value. Use 240 ohms for a base current of 15.4mA.
The circuit is just a logic inverter ... and this is the circuit diagram ... **broken link removed**
I found a datasheet for the old 2N2222 from Central Semi and it shows a max saturation loss of 0.4V when its collector current is 150mA and its base current is 15mA. Then its base-emitter voltage has a max of 1.3V.