Convert the first term into a fraction greater than one.

$2\frac{5}{8}=\frac{21}{8}$

For the second term, start with the problem inside the parentheses.
What is the lowest common multiple of $8$ and $5$?

$\frac{7}{8}+\frac{4}{5}=\frac{35}{40}+\frac{32}{40}=\frac{67}{40}$

Do the multiplication in the second term.

$\frac{1}{2}\left(\frac{67}{40}\right)=\frac{67}{80}$

Subtract.

$\frac{21}{8}-\frac{67}{80}=\frac{210}{80}-\frac{67}{80}=\frac{143}{80}=1\frac{63}{80}$

$1.21$