Creating stable 72V power source
As others note - these devices are made to be chained so supply voltages are in parallel and data lines are daisychained.  

You MIGHT be able to series connect the power supplies (MIGHT) but the data feed would at best not work and quite possibly this would 'destroy stuff'
See data sheets and application note links below for correct operation.

You need a single 5V supply.
ALL devices are in parallel supply wise.
Then daisy chain the data lines in substrings as desired.
eg all 60 powered by 5V, in 5 strings of 12, with 5 data feeds. 

WS2812 datasheet &amp; here

Sparkfun hookup guide

How To Control WS2812B Individually Addressable LEDs

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  I know that parallel power is the conventional way of setting this up, but I cannot find anywhere in the links why series power will not work. 


There is nowhere in the links that says series power WILL work.
And if you just connect them it will not work.
(Data sheets and application notes generally focus on what you should do and/or 
 can do.
They tend not to mention what you can't do, or what you really really shouldn't do.
They often have "absolute maximum" ratings. Connecting the LEDs in series directly very substantially exceeds some of the absolute maximum ratings. This is liable to be a very very bad idea :-).

The Din and Dout leads are reference to ground (5V -ve) for the related IC.
If you series the power feeds then then if say LED1 is at 0/5V, then
LED 2 is at 5/10V,
LED3 is at 10/15V ... then     

LED1_Dout swings 0-5V,
LED2 expects to see 5V-10V on Din
so the Dout from LED 1 is 0/-5V relative to LED2 ground.
This will not work and may destroy either or both LEDs.   

If you chain them the other way with Vout descending then
LED2-Din sees +10/+5 which also will not work and may destroy one or both LEDs. 

While you could TRY to level shift the voltages up or down in each of these cases, it may not work and may still cause magic smoke. 

ALSO series connecting the power supplies if the devices draw differing currents (as they will at various times) will with a supply of N x 5V, result in more than 5V across the low current devices.
You could eg place a 4V7 zener across each LED supply - and it MAY work, but you are building a super non standard arrangement for no apparently good reason. 

I could make this work if I had to (after 50+ years of playing a small amount of magic ability is granted) but I'd not consider trying unless there was an utterly utterly compelling reason to do so.
I can't see that there is