Is there anything wrong with this simple circuit ? Transistor + LED
It is not a good idea to use one resistor for both Leds. By this way you will have different brightness when both are activated. Connect the anode directly to +5V and add a resistor between the cathode and the collector of each transistor.
On the other hand, add for each transistor a high value resistor between the base and the ground. It is a bad design to let the base floating.