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

\(\frac{5}{3} = \frac{{65 - {T_s}}}{{57 - {T_s}}}\)

\(285 - 5{T_s} = 195 - 3{T_s}\)

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