How many atoms are in 5 grams of Fe2O3

There are two iron atoms and three oxygen atoms in each molecule of Fe2O3. So that's five atoms per molecule.

One mole of any molecular substance contains 6.02 * 1023 molecules. Since there are two iron atoms in each of the molecules we're considering, there will be (6.02 * 1023) ⋅2=1.204 * 1024 iron atoms in a whole mole of them.

But we're considering 0.550 mol, so multiply by 0.550:

n = (0.550 mol) ⋅ (3.01 * 1024 atoms/mol) = 6.62 * 1023 iron atoms.