Overall, the strategies you employ for the 5-6 player expansion aren't much different from the original. However, the addition of more players and the ability to build out-of-turn mean there are couple of adjustments players should make in order to be more successful.
Trading with the mother country - In the expansion, ports are much less valuable. The reason for this is you only get to use them once every 5-6 turns instead of once every 3-4 turns. When I play a 5-6 players game and heavily rely on a 2:1 port, I often find myself discarding half of my hand in the end game because a seven is rolled before I even get a chance to convert all those resources into what I need. Ports are still useful and should not be neglected entirely, though. Just don't value them as highly as before, and especially try to stop yourself from placing a starting settlement on one. One other thing to notice about ports is that there are now two 2:1 sheep ports, so you have a better chance of getting access to one. so, remember to look more closely for getting access to a 2:1 sheep port if you have access to a lot of sheep.
You don't need the longest or biggest to be the bestest - In the expansion, there is much heavier competition over the longest road and largest army. It's still awesome to get one of those, though competition will be much more fierce. Be prepared to invest heavily to get those +2 VP. As such, you may want to focus those resources elsewhere, especially at the beginning of the game. In a 5-6 player game you won't need one of those bonuses in order to win, but to win without them you will need an extra emphasis on early expansion.
Trade your way to the top - In the five to six player expansion you have a much greater chance of finding someone who needs what you have and has what you need, than you did in the original Settlers of Catan. So, be even more aggressive with your trading. Remember that people will be using ports less, so those who rely on them will sometimes need to offload extra resources to avoid losing half of their cards.
One extra bit of sneakyness - In the expansion you're still only allowed to play one development card per turn. However, you now have the opportunity to buy the development cards between turns, and I suggest you don't forget that. Sometimes buying a development card right after the turn of the person before you and then playing it immediately afterwards on your turn before rolling the dice can come in quite handy.
Well, that's about it. Since the expansion doesn't add many rules, the strategy is very much the same as before. You'll do well as long as you remember to go for brick/wood or stone/wheat, expand early, and place those initial settlements well. As always, feel free to post on the forum if you have any comments / questions / criticisms. If you enjoy the five to six player game and haven't tried Cities and Knights of Catan yet, I highly recommend you check it out.