Tail lights wont come on keeps blowing fuse blows 10 amp 15 amp and even 5 amp fuses

fuses blow because of dead shorts or excess current draw
to blow a 15 amp fuse indicates a dead short
by disconnecting the rear lights , the problem is in something else you have replaced
could be a problem in the head light wiring

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do you have acell phone or other charger plugged in or multiple chargers?? i seen so many that draw way to much and keep blowing fuses. we've run several hot sockets direct from the battery to provide power for such dont forget to fuse it !

Look for shorts in the circuitry.

Check your tail light and other running light sockets for corrosion.
Pull each and every bulb to check it, also check the back side of the socket.
(Your headlights are not part of this circuit.)
Rust or water with rust will conduct enough current to blow the fuses.
Please revert back to the 20 amp fuse, as you may damage the wires leading to the bulbs in places you won't be able to find or fix.
It's unlikely that it's one of the actual light bulbs, all light bulbs tend to go open instead of shorted, but you can check them too.

The fuse doesn't blow till you turn on the light switch? If it blows before turning on light switch, look for a short to ground between fuse box and light switch.
If it blows after turning on light switch, I believe they make a short finder tool.

That was my first thought, too. But it would not "fry" the whole circuit, so don't give up yet, using the higher fuse may have just cost you one more step of finding the problem.
So is it still blowing a 10 amp fuse? Either way what you really need is someone with a voltmeter or multi-meter to track down where the power has been lost. Most cars have the tail (or park lights) and the dash illumination lights on the same circuit, therefore using the same fuse, so an electrician could start by checking if the fuse has power with tail light switch on, then checking the wire going up to the dash, and how the tail lights wire is spliced with that or separately from the fuse and then routed to the rear.
It always helps to have a wiring diagram, sometimes absolutely necessary with involved circuits. Your problem should be simpler, not so much to look after, although the colors of the tail light wires may be needed. The person with the voltmeter can follow the wires that way, sometimes you have to pull a harness apart to find the wires you need. It may take a little time, but anyone who knows how to use a voltmeter should be able to find the problem. It does take time, sometimes, alas.

Brake light shorted to ground.

put a higher amp fuse in it, also is there any other added mechanisms put in the car? if so, they may be draining amps from the fuse

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