Wiring 5 LED Lights in Parallel
It appears that you're taking individual wires out of cables and running them in different directions. Don't do that.
From S1 (see labeled image, below), you've got your red &amp; black travelers running toward S2, but you've got the white (I presume that's what the orange line represents) going to C5. Disconnect the white/neutral from C5 and allow it to pass through the box and on with the travelers to S2 as below.
From C5 to C1, it appears that you're using 12/2 and repurposing the white wire as a traveler. Replace this piece of cable with 12/3 (remove the 12/2 so there's no confusion in the future), carry the neutral from C5's box through to C1's box.
It appears that you've got 12/3 from C1 to S2, but that you've again split the wires from the cable to attempt to use them for different purposes. Don't do that! Use this piece of 12/3 (in its entirety, black, red AND white) to continue to carry your supply power to S2 and wire up the 3-way switch there properly.
Now that you've got your travelers properly set, you've got switched power at S2. Run an additional 12/2 from there to C1, pig-tailing the black/hot to the hot on the bulb (as you've got) and add a pig-tail from the white/neutral to the neutral on the bulb.
You should be good to go at C2, C3 and C4 with exactly what you've got.
Back at C5, make sure you've disconnected the existing white/neutral from the switch and tied it into the new 12/3 running toward S2. Tie the white/neutral coming from C4 to the bulb on C5.
Don't laugh, I drew the lettering with my thumb-operated track ball.
Additionally, I'm presuming that you've got the bare ground wire properly connected. The grounds should be connected from cable to cable, and it should be pig-tailed to each device (switch or light). It should be connected in a daisy chain, following the supply of power. You may be tempted to connect all the grounds in C5 together (both those coming from S1 and from C4). I do not believe you should do that, though I'm not certain that it will cause harm - I'll let the electricians chime in on that. I wouldn't do it, and it would work properly with them separated. I'm pretty sure it would be safe if they're connected there, but I'm not sure that it's code compliant that way.