5. The number of 5-digit natural numbers, divisible by 5 and which have the sum of the first two digits equal to 5, is:
A. 1000
B. 3200
C. 1600
D. 400
E. 800
Solution: Let $A=\{0,1,2, \ldots, 9\}$. The numbers we are looking for are of the form $\overline{a b c d e}$; $\overline{a b} \in\{14,23,32,41,50\}, c, d \in A, e \in\{0,5\} ;$ using the product principle we get $5 \cdot 10^{2}=1000$ numbers.