Depends on what sort, but you'll probably have to multi-class in whatever you need. Magic in 5th is a lot more renewable and castable, so it's heaps closer to a 3.5ed psion. But telepathy isn't one of the edition's strong points. But illusion is, which can simply be you warping minds as you want.
Maybe also consider a cleric or druid level or two, just to expand the spell lists. They can get some fairly nice front-loading going at lvl 2 for extra quirks. It depends on how you RP the powers given.
So levels in wizard, sorcerer, warlock, bard, cleric or druid should give you the tools for the character. There's heaps of different sorts of telepath, so it's pretty hard to give better than generic advice unless you state a more thorough character outline than "telepath".
Take friends, prestigation and minor illusion as cantrips, write them off as mind warping, grab charm as a spell and go from there.