I agree with @winwaed, it certainly looks like a pepper plant and all peppers are safe to eat. If 'you're told it was cayenne', that will be as close you're going to get as identifying the exact species I'm afraid. The fruits should be long, thin, and hanging downwards.
I've grown many dozens varieties of peppers, ordered from respected distributors, and even then on multiple occasions the pepper eventually turned out to be a different kind of species as ordered. (ie. scotch bonnet which turned out to be bishops crown, as we identified together with the distributor, by the partially purple flowers).
So if this is 'really cayenne' is impossible to say I'm afraid, but maybe that's not just that important... Just have fun growing them and give them a taste! :-)