Hard to say; the HBO series has started relatively strong, retained its viewers, is being lavished with critical acclaim and positive word of mouth, seems exactly like the kind of series that could see a boom following DVD release exposing it to a larger audience, and has an established base of book readers to draw from that it itself is simultaneously feeding back into. General consensus is that books 2 and 3 are even better than book 1, so not unreasonable to think the buzz will only keep growing if they maintain this level of quality. 6 or 7 seasons is an incredibly difficult feat for any TV series to pull off, much less one that involves such a large cast and that we know will (or should, at least) require increasing special effects costs, but given it's HBO and with the start so far, I'd say the odds aren't horrific that it can pull it off.
That said, while I agree with deaconson that they won't be able to do a straight 1 to 1 conversion with books 4 and 5, and will likely need to adjust season length as soon as next year just to handle book 2, I don't know that breaking books into multiple seasons is feasible. The casting contracts are going to be difficult enough to deal with as is assuming success that subsequently raises everyone's profile. Also, there's simple problem of dealing with the actors aging; show's already seen one actress die and was just lucky it was for a minor character done after book 1 anyway, and even moreso, the kid actors, which they already casted several years older than the book, aren't going to stop growing. I think they'll just have to merge the perspectives of books 4 and 5 while maintaining them as 2 different seasons, and start going with season lengths of about 12, give or take, episodes.
