$$\displaystyle{\left(-{10}{x}^{{4}}+{8}{x}^{{3}}-{x}^{{2}}+{10}{x}\right)}+{\left(-{8}{x}^{{3}}-{5}{x}^{{2}}-{4}\right)}$$

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We need to find the given sum of polynomials
$$\displaystyle{\left(-{10}{z}^{{4}}+{8}{x}^{{3}}-{x}^{{2}}+{10}{x}\right)}+{\left(-{8}{x}^{{3}}-{5}{x}^{{2}}-{4}\right)}$$
Remove the parantheses using (-a)=-a
$$\displaystyle-{10}{x}^{{4}}+{8}{x}^{{3}}-{x}^{{2}}+{10}{x}-{8}{x}^{{3}}-{5}{x}^{{2}}-{4}$$
Now group the like terms (terms with same exponent of x)
$$\displaystyle-{10}{x}^{{4}}+{8}{x}^{{3}}-{8}{x}^{{3}}-{x}^{{2}}-{5}{x}^{{2}}+{10}{x}-{4}$$
$$\displaystyle-{10}{x}^{{4}}+{\left({8}{x}^{{3}}-{8}{x}^{{3}}\right)}+{\left(-{x}^{{2}}-{5}{x}^{{2}}\right)}+{10}{x}-{4}$$
$$\displaystyle={\left(-{10}{x}^{{4}}-{6}{x}^{{2}}+{10}{x}-{4}\right)}$$
The sum of the polynomials is $$\displaystyle{\left(-{10}{x}^{{4}}-{6}{x}^{{2}}+{10}{x}-{4}\right)}$$