You won't be able to shock yourself with 12v, but you can shock yourself with whatever power supply you find that'll do 5A at 12v. Assuming you'll only use one strip at 6a just grab a laptop power supply (I'd recommend this one: http://www.newegg.com/Product/Product.aspx?Item=N82E16812203037) - that way you really don't need to worry about whatever engineering decisions went into building that laptop power supply.
If you cleanly splice the wires, you won't have any issues. Solder them correctly, twisting them to have a mechanical connection and soldering to have an electrical connection.. then heat shrink it.
The LEDs will not give off enough heat to catch on fire or burn your bed, ever.
This project could easily be the fusion of 2 well engineered products to do something cool without any risks! Have fun!
What watt power transformer should I be using?
You can use a power supply like the one pictured, rated for the amount of LED's you will be driving. Read the specs on the lighting. They should tell you how many watts per a given length of the strip. So if it says, for example, that needs about 1 watt per meter, then a 15-foot section would require a 5 watt power supply. Take your total length of 76 feet, and divide by the strip's requirements. It wouldn't surprise me if you ended up somewhere in the ballpark of 20 to 30 watts.
Can I run 14 gauge wire directly from a circuit 15 amp breaker to the transformer?
No. You can't put the power supply inside the wall, and you can't bring the wire out of the wall without going through a junction box. The best way to do this is to put a cord on that power supply, and plug it into an existing outlet. There is no need whatsoever to add a new circuit or connect these directly to a circuit breaker.
Can I plug in all 5 circuits of LED strips on top of each other to the output of the transformer?
Yes, you can wire multiple strings in parallel at the power supply. If the sections are short, you can also wire them end-to-end. Double-check the specs for maximum length of a single run.
Is this the recommended way of doing what I'm trying to accomplish?
The recommended way is to plug into an existing outlet. If your lighting requirements added up to 1000 watts, you'd want a new circuit. At 20, 30 or 50 watts, it is ridiculously small in household circuit requirements.
I would also like to add a on/off switch, do they make a wall switch for 12v?
Any switch can be used for 12v. I would put the switch before the power supply. Put a cord on the power supply like this cord with switch.
Can low volt wires come right out of the wall, or do they need a junction box before being connected to the LED strip lights?
The low voltage wires don't need a junction box, but they do need a junction plate, like those used for phone jacks.
Best Answer
Was it very bright, once, and now it doesn't light? That was you frying it.
LED strips do not have switching regulators on them, current limiting is done by dumb resistors. They are running at absolute limits on 13.8V which is float voltage for an automotive alternator.
Looks like you're out $22. Sorry.
Now if you really need to run off 19v, you can buy a type of LED strip designed to run on 24V. Those will be notably dim, but it's worth a try.