Powering 39 LEDs via PCA9685

Does a PCA9685, via supplying 5V to the terminal blocks in the of middle board, power the LEDs at each output pin?

At first I thought this was the case but I built the circuit and LEDs stay illuminated when I disconnect the 5V to the terminal blocks. I assume you can't connect too many LEDs to one MEGA.

In my project I want to control 39 LEDs individually. How would I go about this?

Best,

Tony

Use individually addressable LEDs such as WS2812. No need for the PCA9685

take a LED driver like a MAX7219 (for up to 64 LEDs), or a HT16K33 (for up to 128 LEDs), several SX1509 (for up to 16 LEDs each) or addressable LEDs like already mentioned.

More information required. Individualized intensity, or just on/off? On/off could be done in any number of ways, as others have alluded to. Are these LEDs co-located, or scattered across a room?
Are they pulsating, on for hours, or ??