I don't know how you came up with needing 5 V, but it sounds like a bad idea. You have a big efficiency problem, so spending a bit more on power electronics will make things easier and cheaper in the long run.
First, I would not bus around power as low as 5 V because that will require too much current. Having a roughly 48 V bus sounds like a much better idea. Each panel can then locally convert that to the specific voltages needed to run the LEDs and the electronics. That also gets around the problem of the bus voltage drooping from the power supply to the panels and between panels. The buck supplies on each panel can tolerate significant variations in the "48 V" power bus. And, because of the lower current there will be less variation in the first place.
Look at what voltages the LEDs need. Red and green will be near 2 V, but blue over 3. Red and green are probably close enough so that you can use one power voltage for both of them. Green has the higher voltage, usually about 2.1 V, so make a little more than that. You want it only high enough so that you can put enough of a resistor there to have the current be reasonably predictable despite variation in the LEDs. Maybe 2.5 V is a reasonable tradeoff. Red LEDs usually drop a bit under 2 V, so the regulation for red will be slightly better. Either way, this is still way better than 5 V. For the same LED brightness, just switching to 2.5 V instead of 5 V will save half the power.
Blue usually requires significantly more voltage, like over 3 V. Make a separate supply for blue. It should be a few 100 mV above the LED voltage, just like for the red and green LEDs.
48 V is a common voltage for off the shelf power supplies, and is the limit you are usually allowed before you get into legal regulations. There are various buck converter chips out there, or if you're clever you can maybe have a existing micro handle the buck conversions. Either way, these are readily available blocks you can use in your circuit.
From your description, it seems you need to debounce the switch.
You can do this
Since you seem to be using some kind of resistive ladder to read multiple buttons on one ADC port, this will be a little more complicated.
If they can all be on the same amount of time, I'd just use lots of shift registers. There are several types. For your application look for Serial In, Parallel Out (SIPO).
If it mattered how bright the LEDs are, and you want very bright, use 'proper' LED display drivers.
For example TI Display drivers
They come in 8-LED, 16-LED and even 24-LED devices.
A SIPO shift register can be chained together by driving them all from a common clock, and connecting Serial Out of one device to Serial In of the next device. They may also have an enable which trasfers the shifted bit pattern into the LED drivers.
Initialisation, power on, must clear all of them to zero (usually a RESET), and initially load a 1 to the first shift register.
Edit: Removed concerns about 4017, as they don't apply.
A datasheet for 4017 which shows a schematic for cascading three (and hence more) 4017 in Figure 12 page 15.