Answer
The answer is $2280$.
Work Step by Step
For the first series ${a_n}=-5,10,-20,40,...$.
Common ratio $r=-2$.
This is the geometric series.
Sum of the first $10$ terms.
$S_{10}=\frac{-5(1-(-2)^{10})}{1-(-2)}$.
Simplify.
$S_{10}=1705$.
And the second series is ${b_n=10,-5,-20,-35,...}$.
Common difference $d=-15$.
The tenth terms is.
$T_{10}=10+(10-1)(-15)$
Simplify.
$T_{10}=10+9(-15)$
$T_{10}=10-135$
$T_{10}=-125$
The sum of the first $10$ terms is
$S_{10}=\frac{10}{2}\cdot (10-125)$
$S_{10}=5\cdot (-115)$
$S_{10}=-575$.
The difference is $=1705-(-575)$
$=2280$.
