Replacing 5 gang light switches that have 3 of them daisy chained together
The leftmost switch is completely separate, and its wires (including neutrals) need to be kept completely separate.  In this case, power comes into the box on one cable, and onward to the lamp on the other cable. Hook that up as you found it, and maintain a "hard wall" (virtual or physical; they make physical partitions for boxes) between those two cables and all the other wires in the box.  It is probably on a different circuit. 

On the right side, the red wire from the wall is being split to serve the hot side of all 4 switches.  The mechanical method being used is to "daisy-chain" jumpers from one switch to the next, since the switch appears to support 2 wires per input. This is functionally the same as pigtailing; do either one as you please. 

If in doubt, I recommend pigtailing, because it's easier for novices to understand.



Oh, that switch on the right in the photo.  That is a 3-way switch.  Black screw is common, and when replacing them, which wires go to which color screws is a huge deal. Position is useless since every switch model randomizes the positions.  If you are using it as a plain 1-way switch, use black and only 1 brass. If it's up when it should be down, use the other brass, or just flip the switch over.