Answer
$a_{5} = -10$
Work Step by Step
$a_{n}$ of the arithmetic sequence is $a_{n} = a_{1} + (n-1)d$
Given $a_{4} =-5$
$a_{10} = -35$
$a_{4} =a_{1} + (4-1)d$
$a_{4} =a_{1} +3d$
$a_{1} + 3d = -5$ Equation $(1)$
Similarly,
$a_{10} =a_{1} + (10-1)d$
$a_{10} =a_{1} +9d$
$a_{1} + 9d= -35$ Equation $(2)$
Subtract Equation $(1)$ from Equation $(2)$
$a_{1} + 9d - (a_{1} + 3d)= -35 -(-5)$
$a_{1} + 9d - a_{1} - 3d= -35 + 5$
$6d = -30$
$d = -5$
Substituting $d$ value in Equation $(1)$
$a_{1} + 3d = -5$
$a_{1} + 3(-5) = -5$
$a_{1} -15 = -5$
$a_{1} = -5+15$
$a_{1} = 10$
Using $ a_{1} $ , $d$ values and $n=5$ ,
$a_{5} = a_{1}+(5-1)(-5)$
$a_{5} = 10+(4)(-5)$
$a_{5} = 10-20$
$a_{5} =-10$
