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discount of 5% means selling price is now 0.95n
To make a profit of 10%, (selling price - cost price)/cost price *100% = 10%
Assuming we are marking up the cost price by y%, so

To get an effective 10% profit,
(95/100)(100+y) - 100 = 10
y = 15.6%
He should mark up his price by 15.6%, so that after 5% cash discount, he gets an effective 10% profit.

Let me solve it another way to confirm, I'll use the famous number substitution

Cost price = $100
Marked up by x%, so needs to mark up by (x/100)*100 = $x
SO marked up price is $(x+100)
If cash payment is made, 5% discount, so selling price is 0.95(x+100)

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