According to $Newton's$ law of cooling

$\frac{{{T_1} - {T_2}}}{t} = K\left( {\frac{{{T_1} + {T_2}}}{2} - {T_s}} \right)$

For first $5\,minutes,$

${T_1} = {70^ \circ }C,{T_2} = {60^ \circ }C,t = 5\,minutes$

$\therefore \frac{{70 - 60}}{5} = K\left( {\frac{{70 + 60}}{2} - {T_s}} \right)$

$\frac{{10}}{5} = K\left( {65 - {T_s}} \right)$                    $...(i)$

For next $5\,minutes$

${T_1} = {60^ \circ }C,{T_2} = {54^ \circ }C,t = 5 minutes$

$\therefore \frac{{60 - 54}}{5} = K\left( {\frac{{60 + 54}}{2} - {T_s}} \right)$

$\frac{6}{5} = K\left( {57 - {T_s}} \right)$                       $...(ii)$

Divide eqn. $(i)$ by eqn. $(ii)$ , we get

$\frac{5}{3} = \frac{{65 - {T_s}}}{{57 - {T_s}}}$

$285 - 5{T_s} = 195 - 3{T_s}$

$2{T_s} = 90\,\,or\,\,{T_s} = {45^ \circ }C$