Hello Ash,
The energy in electron shells closest to the nucleus (n=1,2,etc.) are lower in energy and the electron shells farther from the nucleus (n=4,5,6,etc.) are higher in energy. Remember, for an electron to move from a lower energy level to a higher energy level, energy must be absorbed. For an electron to move from a higher energy level to a lower energy level, energy must be released or emitted.
Therefore, this statement is false.
I hope this helps!