The slope of Arrhenius Plot (lnkv/s(1)/(T)) of first order reaction...

Arrhenius equation is $k = {Ae}^{- \dfrac{{E}_{a}}{RT}}$

So, $lnk = lnA - \dfrac{{E}_{a}}{RT}$

This is a straight-line equation of form $y = mx + c$

where $y = lnk, x = \dfrac{1}{T}, m = - \dfrac{{E}_{a}}{R}$ and $c = lnA$

$m = - \dfrac{{E}_{a}}{R}$

$- 5 \times {10}^{3}K = - \dfrac{{E}_{a}}{8 . 314}$

${E}_{a} = 8 . 314 \times 5 \times {10}^{3}{Jmol}^{- 1} = 41 . 5kJ{mol}^{- 1}$