Verified answer

[tex]\displaystyle\bf\\\frac{2ab^{2}-10b^{2} }{a^{2}-10a+25 } =\frac{2b^{2}\cdot(a-5) }{(a-5)^{2} } =\frac{2b^{2} }{a-5} \\\\\\b=1 \ \ , \ \ a=8\\\\\\\frac{2b^{2} }{a-5} =\frac{2\cdot 1^{2} }{8-5} =\frac{2}{3}[/tex]