NaOH is a strong base therefore it completely ionises to give out hydroxide ions.
Number of moles of NaOH added - 5.3 g / 40 g/mol = 0.1325 mol
molarity of NaOH - 0.1325 mol/1.5 L = 0.088 mol/L
since NaOH --> Na⁺ + OH⁻
molarity of OH⁻ is 0.088 M
we can calculate pOH value to find the pH value and then [H₃O⁺]
pOH = -log (0.088 M)
pOH = 1.05
pH + pOH = 14
Therefore pH = 14 - 1.05 = 12.95
[H₃O⁺] = antilog (-pH)
Therefore
[H₃O⁺]= 1.12 x 10⁻¹³ M