$ 解:設(shè)半圓S_{1}的半徑為r_{1},半圓S_{2}的半徑為r_{2}$
$∵S_{1}+S_{2}=\frac{17}{8}π$
$∴\frac{1}{2}π×r_{1}2+\frac{1}{2}πr_{2}2=\frac{17}{8}π$
$∴r_{1}2+r_{2}2=\frac{17}{4}$
$∵AC+CB=5$
$∴r_{1}+r_{2}=\frac{5}{2}$
$∴(r_{1}+r_{2})2=r_{1}2+r_{2}2+2r_{1}r_{2}=\frac{25}{4}$
$∴r_{1}r_{2}=1$
$∴S_{△ACB}=\frac{1}{2}×(2r_{1})×(2r_{2})=2r_{1}r_{2}=2$
