Can we say:
"Before I became a singer, I had been a hall monitor for almost five years at the Stuart Little Elementary School for the Musically Inclined Children."
Instead of:
"Before I became a singer, I had been a hall monitor at the Stuart Little Elementary School for the Musically Inclined Children for almost five years."
The usual order for location and duration is to put the location first. See this grammar note from Cambridge Dictionary and this web page for English language learners.
However, if the phrase giving the location is considerably longer than that giving the duration, as it is in your example, then it would generally be better to put the duration first.
How much longer does it need to be for you to put the duration first? It's a judgment call—there's no standard formula. But for your example, Stuart Little Elementary School for the Musically Inclined Children is much longer than almost five years, so in this case, putting the duration first will lead to a more comprehensible sentence.
There are also other reasons you might want to put the duration first. For example, if the next sentence of your writing explains more about the location, then putting the location last will connect the two sentences better.
Both the other answers hint at this, but let me state it explicitly ...
Both sentences in the question are grammatical. Which one to prefer depends on how you intend to continue.
Choose this variant
Before I became a singer, I had been a hall monitor for almost five years at the Stuart Little Elementary School for the Musically Inclined Children.
if you intend to start the next sentence with a mention of the school or of the children, perhaps
Before I became a singer, I had been a hall monitor for almost five years at the Stuart Little Elementary School for the Musically Inclined Children. Musically inclined they might have been, but they were ghastly little oiks, exceeded only in ghastliness by their parents.
Choose the other variant
Before I became a singer, I had been a hall monitor at the Stuart Little Elementary School for the Musically Inclined Children for almost five years.
if your next sentence starts with reference to the five years, perhaps
Before I became a singer, I had been a hall monitor at the Stuart Little Elementary School for the Musically Inclined Children for almost five years. And they were the five happiest years of my life.
Placing it at the beginning is fine, though in your example it sounds less idiomatic. In general, the context matters. For instance, which information the author wishes to emphasize.
