When an electron absorbs energy and is in a higher energy orbit (I guess the atom would be in an unstable state), when the electron releases this energy, would all of this energy be released at the same time, or could it release energy one "level" at a time?
So for example if a Hydrogen atom absorbed a lot of energy and its electron went to some level n = 5, could it slowly make its way back down to level 1?
Yes, it certainly can. In fact, it can do either, traverse gradually across excitation states down to its ground state, or jump from its current state to its ground state, or to any lower state for that matter. So essentially, as long as the target state is equal or lower in energy than the current one the electron can jump to it.
Those jumps have different probabilities though. Determining which process is more likely to occur, and what the probabilities are is a matter of quantum mechanic calculations. Have a look here for example: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/fermi.html
To add to @Tanith Rosenbaum's answer, the energy can be lost to other energy levels by emitting a photon to that other level, say n = 4 to 3. The total energy is conserved, thus the energy of atom in n=3 + photon is the same as that of the atom in n = 4. Emission (fluorescence) is a spontaneous process, and the lifetime of an excited atom can vary widely, typically from nanoseconds to seconds. The reason for this depends on symmetry and angular momentum of different energy levels (generally called selection rules).
To loose energy in any other way, say by collision with another atom, then that atom has to carry away the difference in energy just as the photon did. Note that a collision can also add energy by the same reasoning, as can absorbing a photon so the atom will now contain even more energy. In a more detailed examination, properties such as symmetry and angular momentum have to be considered.
