Powering a long 20M LED strip light run in large room through ambient lighting via crown molding
They make a lot of socket connectors and other kit for novices.  Unfortunately this product is a bit too &quot;out there&quot; and I wouldn't expect to find stuff like that.  You'll have to do it old-school, by soldering leads onto the solder pads.
Solder on short (&lt;12&quot;, 6&quot; is better) #20 or #22 wire pigtails, stranded if possible. Otherwise the wire is too stiff and it tends to &quot;wag the dog&quot; i.e. the wire pushes he strip around and can even tear the solder pads off. I know that wire seems awfully light but it's OK for a short pigtail as long as you keep current below absolute limits for that wire (under 5A for #20... or under 3.5A for #22...)
Those tie onto the feeder wires.  At such short distances voltage drop won't be an issue.
What you really have there is 5 channels plus a &quot;common&quot;.  Now, 3-channel amplifiers are ubiquitous.  4-channel (RGBW) amplifiers can be had.  5-channel, forget it.  You'll be forced to use two 3-channel amplifiers, which is fine.  You don't need to distribute the amplifiers all over the place if you have a big enough central amplifier to drive the whole shebang and are willing to run 6 feeder wires.  You'll want to make the common extra large; it's carrying 5x the current of the others...