Analog Led Audio Spectrum Analyzer Simulation
You have supply pins connected to U2 and U3 but you've forgotten to connect them to U1. 

C3 smooths the rectified voltage from the emitter of the BJT. In other words it's a cheap and inaccurate signal peak detector with C3 as the hold capacitor (go google this). R5 is needed by the BJT and also offers a discharge path for C3 in order to allow dynamic signals to refresh the display. If it wasn't there you'd have a peak-hold circuit.