Answer:

First, let's calculate the mass of NaOH:

Molar mass of NaOH = 22.99 + 15.99 + 1.008 = 40.98 g/mol

Mass of 5 mol NaOH = 5 mol x 40.98 g/mol = 204.9 g

Next, let's calculate the total mass of the solution:

Mass of NaOH + mass of water = 204.9 g + 20 g = 224.9 g

Now, let's calculate the mole fraction of NaOH:

Moles of NaOH = 5 mol

Moles of water = mass of water / molar mass of water

Molar mass of water = 2(1.008) + 15.99 = 18.02 g/mol

Moles of water = 20 g / 18.02 g/mol = 1.11 mol

Total moles in solution = moles of NaOH + moles of water = 5 mol + 1.11 mol = 6.11 mol

Mole fraction of NaOH = moles of NaOH / total moles = 5 mol / 6.11 mol = 0.818

Therefore, the mole fraction of NaOH in the solution is 0.818.