Do you live in an area where you can drop off your tv to a licensed repair shop for warranty issues? Can you physically get your tv there? Would you be content with one year of coverage? If you do not buy it and it breaks after a year, can you afford to buy another at full price or pay for a repair?
If you answered "no" to any of these, buy the plan.
You also most likely will get some sort of price break on other things and/or coupons which do the same. The only difference in the 3 or 5 years plans is usually just the term; the same problems are covered equally in each plan.
Both plans will be renewable after the term expires, but it will cost you significantly more to get two 3 year plans than it would to get one 5 year plan (even more than what that extra year would cost if you broke it down year by year).
I've never been a big fan of these protective plans that these stores offer. But I'm wondering if I should with the purchase of a 50+ inch HDTV. I'm leaning toward an LCD (Sony) but my main question is wether to buy the extra protection where if they can't fix it they will replace it? Should I worry about dead pixels and other issues and pay the extra money. Are the screens an issue or are they handling the test of time (reliable) and if you do recommend on one should i pick the 3 or 5 year plan?