Answer
The Young's modulus for this wire is $7.69\times 10^{10}~N/m^2$
Work Step by Step
$Y = \frac{F/A}{\Delta L/L}$
$Y$ is Young's modulus
$F$ is the force
$A$ is the cross-sectional area
$\Delta L$ is the change in length
$L$ is the original length
We can find Young's modulus:
$Y = \frac{F/A}{\Delta L/L}$
$Y = \frac{F~L}{A~\Delta L}$
$Y = \frac{(1000~N)(5.00~m)}{(0.100\times 10^{-4}~m^2)(6.50\times 10^{-3}~m)}$
$Y = 7.69\times 10^{10}~N/m^2$
The Young's modulus for this wire is $7.69\times 10^{10}~N/m^2$.
