Both the other answers hint at this, but let me state it explicitly ...

Either sentence in the question is 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.

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.