I think what it really boils down to is:
"Can someone jump as a 5-ft. step?"
I'd say sure. Hopping straight up would be basically like taking a 5-ft. step.
To put it all in nice, even 5-ft. increments:
1) The caster is medium-sized and so occupies basically one 5-ft. cube, and threatens the area 5 ft. around that.
2) Burning Hands can reach a total of 10 ft. from the caster themeslves (and cannot be extended to the caster's reach). Even a Giant casting Burning Hands can't start the spell at the end of his fingertips...the magical energy goes out 10 ft. from the point of origin (the caster) and stops.
3) The enemy in question moved onto the cieling, effectively 15 ft. beyond the caster. The caster can "reach" 5 ft. beyond their own cube. The Burning Hands spell affects that reach, and 5 ft. beyond that. So they can't reach the enemy.
So, right now, the caster can't hit the enemy. It'd be the same thing as if the enemy was 15' away form the caster on the ground. The spell's range is one increment too short.
BUT
As part of her turn, the spellcaster can make a 5-ft. step, which puts the enemy within range. Be it a reaching out with hands, be it a slight hop, be it a home-base slide, be it a bit of a shuffle, be it standing on tip-toes, the spellcaster can adjust her position by 5 ft. to hit the creature.
Of course, as a DM, you're free to rule that a slight vertical hop can't be made as a 5-ft. step. But in this case, I'd say you were being unneessecarily harsh.
I'd say a 5' step can be made vertically, too.
Oh, and for T....jeeze, people, enough petty name-calling....
