Like RE4, but less special.
First things first: if you played the demo for Resident Evil 5, don't trust it. That small part of the game is maybe the worst representative slice a game developer has ever seen fit to show. The demo made the game seem like nothing but a confined, slow shooter that was woefully behind the times. The truth is that Resident Evil 5 is just as great as RE4 was, if not nearly as revolutionary.
The story picks up the main Resident Evil storyline again, treating RE4 as more of a sidestory, making references to "The Kennedy Report" now and again. Wesker is back again, the writing is still corny as all hell, and the plot is still ridiculous. But these happen to be the exact reasons I love the series' storyline. They give off a sort of bad 80's action movie vibe that makes them supremely enjoyable. The fact that the game's presentation is amazing doesn't hurt either. The characters are all highly detailed, the voice acting is superb, and the lighting and environmental effects are great.
The gameplay of Resident Evil 5 is without a doubt the elephant in the room here. And truly, there's not much changed since RE4. But this isn't necessarily a bad thing. What people seem to have forgotten is that the controls in 4 were great. Noone complained back then, so what's wrong now? Though newcomers to the series may be put off by the inability to move and shoot, Resident Evil fans will be right at home. The major changes to the game come in the way of the new inventory system and the addition of a co-op mode. All inventory management is done in real time, no time-stopping briefcases to sort through here. This can take a little getting used to, especially in single-player, but really works well when playing co-op. And make no mistake, co-op is the best way to experience Resident Evil 5. I made my way through the entire game in single-player, and I can confirm that Sheva, your partner, is usually pretty braindead (aside from a brief life-saving moment of brilliance near the end of the game). The entire game is designed for co-op play, with most of the bosses set up to encourage experimentation and coordination between the two players. Also, full disclaimer: part of the final boss encounter in the game involves a QTE in which you punch a boulder repeatedly until you punch it into a lava pool. Just so you know.
A final note: much discussion has been made about racism in the game. While I don't believe the makers of RE5 are racist in any way, there is an area that struck me as interesting. About halfway through the game, you come across a traditional African village where all the zombies are dressed in grass skirts and voodoo masks. It's obvious that Capcom used these traditional 40's movie representations of African natives to create a sense of unease and terror, not to make any kind of racist statement. In the end, the game wraps up the whole Umbrella storyline pretty well, and it'll be interesting to see where it goes from here. But for now, RE5 stands as, in my opinion, the best possible follow-up to one of the best games for the last generation, and even surpasses it in some ways.