The density of the solution is 1.33 g/mL. I keep getting an answer of 4.83m, but the key says that the answer is 7.69m.

In 1L you have 5.83 moles of H2SO4, which is 571.9 g, based on
5.83 mol x 98.1 g/mol.
Next find the mass of water in 1L of the solution knowing that the solution has a mass of 1.33 g per mL or 1330 grams per liter.
1330 g  572 g = 758 grams of water, or 0.758 kg of water.
Molality is moles of solute per kilogram of solvent...
5.83 mol / 0.758 kg = 7.69 molal
5.83 mol x 98.1 g/mol.
Next find the mass of water in 1L of the solution knowing that the solution has a mass of 1.33 g per mL or 1330 grams per liter.
1330 g  572 g = 758 grams of water, or 0.758 kg of water.
Molality is moles of solute per kilogram of solvent...
5.83 mol / 0.758 kg = 7.69 molal

You are correct!