There ARE said to be five apples on the table. (Because 'apples' is plural, we use 'are').

I would say that both "there is" and "there are" are acceptable here. "there is" feels more natural and "there are" more formal. Grammatically, I am not quite sure if or why "there is" is OK. My guess is that what follows "there is said to be" feels like a single notion. Or perhaps the distance between "there" and the plural nouns (4 words) is so long that it doesn't feel like a grammatical mistake.

If it were just one apple: There is said to be an/one apple on the table.

If it were just one apple: There is said to be an/one apple on the table.