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cst199221255yThe official answer is the one given by @theKarlisK, but I liked the approach used by @halfflat better, which is also the way I used when solving. ðŸ˜‰
Congratulations! 
cst199221255yP.S. The paper that this was originally published in gave the answer as 3h45m. How they came up with it I have no idea.

To solve this we have to work under 2 assumptions:
1) both have same length
2) their shape is the same in each level of length(meaning constant burn rate)
So:
Let's say the candle's length is number easily divided by 5 & 6, L = 30(x)
their burn rate would be V[5] = 30/5 = 6(x/h), V[6] = 30/6 = 5(x/h)
remaining candle is L  dL(delta L = how many of the canle burned thus far)
So after t hours L[6]  dL[6] = 5(L[5]  dL[5]), since candle 5h burns faster it's the smaller one. Then we just solve
30  V[6]*t = 5(30  V[5]*t)
30(x)  5(x/h)*t = 150(x)  5*6(x/h)*t
Since all paets of the equation have x we can ommit it as long as x ≠ 0
30  5t = 150  30t ; 25t = 120
t = 4.8(h)
After 4 hours and 48 minutes 
turbod3295y1) Under assumption "longer" refers to length and they are both of the same length, answer is 4h48min.
2) Under assumption "longer" refers to length and both burn at same speed, 4h45min.
3) Under assumption "longer" refers to time, 4h 45min.
Sinces there is no reference to the length on the statements but to their times, I think the 3) assumption is the correct one.
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A puzzle for you guys(not my invention, so contains bugs):
If a 5hour candle and a 6hour candle were lit at the same time, how much time would have to pass before one candle is five times longer than the other?
random
puzzle