The coefficient of $x^5$ in the expansion of ${\left(1+x^2\right)}^5(1+x{)}^4$ is 

${\left(1+x^2\right)}^5(1+x{)}^4$

$\begin{array}{l}=\left({ }^5{C}_0{+}^5{C}_1\right.\left.x^2{+}^5{C}_2{x}^4+\dots \right)\\ x\left({ }^4{C}_0{+}^4{C}_{1}x{+}^4{C}_2{x}^2{+}^4{C}_3{x}^3{+}^4{C}_4{x}^4\right)\end{array}$

$\therefore$ Coefficient of $x^5$in $\left\{{\left(1+x^2\right)}^5(1+x{)}^4\right\}$

${=}^5{C}_2{\times }^4{C}_1{+}^4{C}_3{\times }^5{C}_1=60$