Jesus is the Euro really worth twice the dollar? Shameful.
Anyway, if you really have that kind of startup cash, you are way ahead of most new internet marketers who can barely keep their electricity on.
Don't invest it in any "system" or "course" that's supposed to teach you everything you need to know about marketing, you'll learn very little and besides, you can get most of those courses here on Black Hat world for free
There are about 10,000 things you can do online with $5000 bucks and make a very nice profit, but I'll just give you one quick one.
Go on a freelance site like Rentacoder and get someone to build you a nice looking "bulk traffic" selling site. Maybe duplicate a design like this: get-visitors-now(dot)com, should only cost a few hundred dollars to have created.
There are tons of wholesale sources for traffic which you can buy one million hits per month for maybe $100 bucks.
You resell the traffic as your own website maybe at $29.99 for 30,000 hits or something to that effect.
Take a couple hundred bucks a day and advertise the site under keywords like "buy traffic" "bulk traffic" etc, and you'll make a nice profit everyday.
You'll need a merchant account to process orders, you can go with any one of 500 companies to provide that.
Anyway, bulk traffic companies do very well if they are advertised, some webmasters are stupid and think that buying that many hits will guarantee them a few sales, and some just need the traffic to make thier site look popular.