[tex](x^3-m^2x^2+7mx-5):(x-5)=x^2-4x+1\\\\(x-5)(x^2-4x+1)=\\\\x^3-4x^2+x-5x^2+20x-5=\\\\x^3-9x^2+21x-5\\\\\\x^3-9x^2+21x-5=x^3-m^2x^2+7mx-5\\\\m^2=9\ \wedge\ 7m=21\\\\m=3\ \vee \ m=-3 \wedge m=3\\\\\boxed{m=3}\\[/tex]
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[tex](x^3-m^2x^2+7mx-5):(x-5)=x^2-4x+1\\\\(x-5)(x^2-4x+1)=\\\\x^3-4x^2+x-5x^2+20x-5=\\\\x^3-9x^2+21x-5\\\\\\x^3-9x^2+21x-5=x^3-m^2x^2+7mx-5\\\\m^2=9\ \wedge\ 7m=21\\\\m=3\ \vee \ m=-3 \wedge m=3\\\\\boxed{m=3}\\[/tex]