Nope, you sound just like me when I first started learning about all this stuff.
Just to be clear, it sounds like you tasted your brew before you bottled it?
And it has been "fermenting" for 5 weeks?
And you are prepared to bottle but haven't bottled it yet?
There should be little carbonation at the end of the fermentation phase because the fermenter is not pressure sealed like a bottle or a keg is pressure sealed. It is this pressure seal that forces the liquid to absorb the carbon dioxide (CO2) (carbonation). During the primary fermentation phase, the CO2 is allowed to escape the vessel because during fermentation, A LOT of CO2 is generated - far more than is required to carbonate the beer.
One of the characteristics of beer that is tweaked to perfection is how carbonated it is. One great way to control the level of carbonation that your end product will have is to *first* allow all of the fermentable sugars to be converted to alcohol and CO2 during fermentation and then *second* add a controlled amount of sugar immediately before bottling in a pressure sealed bottle. By adjusting how much sugar you add, you can fine tune how carbonated your final beer is.
So my guess is that after 5 weeks in the fermenter your yeast has consumed all of the fermentable sugars. Generally, this means that it would now be time to bottle. Because your yeast has already consumed all of the fermentable sugars in your wort, if you were to simply pour that wort into bottles, then it would not carbonate because the yeast would not have any sugar to turn into CO2 (and a tiny bit of alcohol). That is why you must now add some more sugar right before you bottle.
Now comes the issue of the yeast still being alive enough to consume that bottling sugar. Yes, there should still be enough active yeast floating in the liquid to carbonate your beer (unless something really weird happened to it).
