An aluminum bar of 8m length and a steel bar of 5mm longer in length are kept at $30_{}^{0}\textrm{C}$ . If the ambient temperature is raised gradually, at what temperature the aluminum bar will elongate 5mm longer than the steel bar (the linear expansion coefficients for steel and aluminum are $12\times 10^{-6}/_{}^{0}\textrm{C}$ and $23\times 10^{-6}/_{}^{0}\textrm{C}$ respectively)?
(a)$50.7_{}^{0}\textrm{C}$ (b)$69_{}^{0}\textrm{C}$
(c)$143.7_{}^{0}\textrm{C}$ (d)$33.7_{}^{0}\textrm{C}$