The coefficient of x⁵ in ${\left(1+{\mathrm{x}}^2\right)}^5(1+\mathrm{x}{)}^4$ is

${\left(1+{\mathrm{x}}^2\right)}^5(1+\mathrm{x}{)}^4=\left({ }^5{\mathrm{C}}_0{+}^5{\mathrm{C}}_1{\mathrm{x}}^2{+}^5{\mathrm{C}}_2{\mathrm{x}}^4{+}^5{\mathrm{C}}_3{\mathrm{x}}^6{+}^5{\mathrm{C}}_4{\mathrm{x}}^8{+}^5{\mathrm{C}}_5{\mathrm{x}}^{10}\right)\left({ }^4{\mathrm{C}}_0{+}^4{\mathrm{C}}_1\mathrm{x}{+}^4{\mathrm{C}}_2{\mathrm{x}}^2{+}^4{\mathrm{C}}_3{\mathrm{x}}^3{+}^4{\mathrm{C}}_4{\mathrm{x}}^4\right)$

$\therefore$ Coefficient of ${\mathrm{x}}^5{=}^5{{\mathrm{C}}_1}^4{\mathrm{C}}_3{+}^5{{\mathrm{C}}_2}^4{\mathrm{C}}_1=5\times 4+10\times 4=20+40=60$