Yes, and no it doesn't have to be a full-time job at $5,000+ a month. Stuff you wrote years ago makes money for you today. That's the beauty of the system. It's a game where the longer you've been at it and the more you've built up, the more you make. Of course you want to keep working on building links to your site and adding content, but I make a good living from Adsense on about an hour a day.
From one website, it is very hard to earn more than 5k. Many people who make thousands have many web sites.
I am also trying to reach my first target $1k from adsense.One of my site which is having good SE traffic is getting nearly $10 per day.
Certaintly, a lot of people make more than $5000 a month. But I can tell you it didn't happen overnight, it didn't happen without hard work, and it didn't happen without good traffic and good content.
I disagree with statements like others are making $5K but not me. It proves to (at least) me that there is no one on DP that is making 5K a month OR is hiding. The question is truly valid; a nice living takes 5K every month in most countries. If we are not making that and spending months/years working 'hard' to earn peanuts like $14 or $25 instead, we better quit this and move on. Remember, you are fired from your job the moment you are proven unproductive. I have raised a similar issue here Come on guys, lets be pragmatic.
I am not making that much at the moment, but hope I will reach that mark very soon. BTW, I am not aware of anyone personally who is making that much.