You can't go through Libya for various reasons at the moment. I would forget going to Algeria ( you need a guide from border to border at many £'s per day as well). Your proposed route would be very adventurous by yourself to say the least, assuming you want to explore the desert and not just the main roads.
In your time frame you could try the Venice to Alexandria ferry if it starts running again (we are waiting on details soon hopefully about that - see the thread in the Sahara section).
Else if Syria is ok, then Italy, Greece, Turkey, Syria. Jordan, Egypt, Sudan would be your best bet if no ferry is running. You'll need to research the rainy seasons as you don't say what time of the year this will be. South Sudan is not dry desert ;p
Remember not all borders are open or safe. Darfour isn't exactly a tourist hotspot at the moment either...
5 weeks is not a long time - do the minimum countries you can to get there and enjoy those you do go to a little more in detail I would suggest.
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