You should definitely at least give it a try. The game is very frequently on sale for less than $10, so even if you don't enjoy it as much as you enjoyed Civ 3, at least you won't be down too much cash. But honestly, I think that you'll definitely enjoy Civ 5 if you enjoyed any of the other Civ games. The core mechanics are mostly the same, but the newer Civilization games are more user friendly and everything is more clear in them. Of course, the game will be a little more fleshed out, as there are new policies, victory requirements, etc. that you need to be aware of, but overall the game is the same as it was before.
I think all of the Civ games are great, there's just a few small differences between all of them. This leads to a slightly new version of the game each time a new one is released, but the core foundation of the series will always be there.
Another great reason to try it is the mods. There are so many fantastic mods out there that really let you play any way that you want. Have you ever wanted to play Civ with a group of Stormtroopers? No problem! How about as Gilgamesh? No problem there either!
The modding community is absolutely amazing and you can customize the game to fit your needs, without or without mods. Definitely give it a try!