[Solution] From $S_{\triangle A B C}=\frac{1}{2} B C \cdot A D=\frac{1}{2} A C \cdot B E$, we have $B C \cdot A D=A C \cdot B E$, which means $(3+b) \cdot 13.75=(a+6) \cdot 16.25$. Also, $b=a+5$. Substituting this into the equation, we can solve for $a=5$. Then $b=a+5=10$. Therefore, $a+b=15$. Hence, the answer is $(D)$.
17.97 As shown in the figure, in $\triangle A B C$, $A D \perp B C, B E \perp$ $A C, A C=16.25, B C=13.75, H E=6, H D=3, b-$ $a=5$, then the value of $a+b$ is
(A) 12.
(B) 13.
(C) 14.
(D) 15.