Are you still sleeping together? You know... the 'for old times sake' thing... or having a little kiss? If so, then no, it's not possible until you knock that on the head.
Five weeks is a relatively short space of time and I would have thought some sort of cooling off period would be needed. Personally, unless there are kids involved, I would not like to be in touch with an ex, I've not enough friends not to want an ex lover as one, they're two different things.
That said, obviously I'm also a complete hypocrite since one of my closest friends is an ex boyfriend from a few a few years bac; mind you, he's a stubbon maschoist clearly and wouldn't let me do my normal 'cut all ties' approach to splitting up as we didn't split up for the normal reasons people do and there was genuinely no animosity. I'm glad that we are friends and I can't imagine us not being friends but those first few months were proper ropey... lots of rows, lots of re-setting of boundries, lots of self control and disciplin... It was hard work. And we slipped up more than once which made it doubley harder... So definitely don't do that.
I guess you have to weigh up how long you were together, what the factors were in the break up and how much you're prepared to making the friendship work. As I said, it's really not easy.