Using an Arduino to drive a digital RGB LED strip
I can not find detailed information regarding the 5M LED strips you bought.

I have used Adafruit addressable LED strips.  What Adafruit publishes on their web site helped a great deal when I cut my strips into smaller sizes.

Here is an Adafruit image which may help you:



I would think the order does not matter.  But you do need to connect the data such that "outs" go to "ins".  And you need to connect them in a row.  That is you need to connect them in one loop.  

Added later...

Assuming we are using the WS2812:



We know from the specifications that the RGB data is encoded as 3 8 bit NZR (Non Zero Return) pulses.  8 bits for each color: red, green &amp; blue.  That there is 1 such "word" of 24 bits for each pixel.  That the beginning of a set of "words" is marked by a 50us or grater interval where DI is zero.  And that each pixel strips off the first 24 bit "word" before passing the balance of the data on. 

In other words, it doesn't matter what order WS2812 are assembled in.  Also that WS2812 have no idea where they are in the sequence.  All that matters is that each succeeding WS2812 gets its data from the previous WS2812. 

One last note. The necessary timing is really fast and really tight. Can't be more than 150 billionths of a second off. No way can a multitasking platform like a PC, Mac or RaspberryPi pull this off.  When sending off a set of "words" to a string of pixels, the embedded processor will likely not be doing anything else!