1 mole of carbon = $6,023 \times {10}^{23}$ atoms [ Avagadro's Number]

so that 

5 moles of carbon = $5\times 6.023 \times {10}^{23}$atoms

                                 = $30.11\times {10}^{23}$ atoms                

Hence 5 moles of carbon contain,   $30.11\times {10}^{23}$ carbon atoms. Hence the correct option is D.