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that will be fine mate
led's use next to no power
this 1 44 Keys 4AX3 12A IR Remote Controller Control RGB 5050 LED Strip 2 connector | eBay remote, will power 12 amps of led's, this equates to around 5m*60led's=300led's , the cig lighter wire is fused at around 10 amps from memory. might recomend running a relay on the cig lighter line or something and running a seperate wire, can use the radio wire or something if prefered, the safest bet for that many LED's is to run a relay though to make sure that it wont blow anything or melt any wires. your call in the end, relays are cheep(ish) and running another wire isnt too hard, but if you melt your cig lighter wires then you might be in a bit more trouble. i recomend a relay personally, especially for that many LED's, even with their low power consumption.
just go to auto one or jaycar or something, just make sure the relay takes 12v. jaycar has these Automotive Fused Relay - SPST 15A - Jaycar Electronics which are fused but i would advise fusing as you leave the battery. you shouldnt need very heavy duty cable (i just used small figure 8. just a matter of making sure that you fuse it. i would recommend a 10A fuse for starters but if that blows, try a 15A. i can take a pic of how to do anything if your unsure and post it here just let me know. you could use a single core wire if you wanted but you would need to use the chassis as the neg terminal. up to you really.
What's wrong with splicing them all together through a normal switch and just having a switched positive...ill send a photo of the wire size i have, coming straight from the battery wont effect it compared to coming from anywhere else. a relay is simply a way to isolate the 2 different circuits and to run them on different amp ratings. relays are just electromagnetic switches that turn on a switch electrically when there is voltage through the switching circuit, the other circuit is active.