Question 1041398
{{{125^(1/2)=5sqrt(5)}}}
{{{(5/64)^(-1/2)=(64/5)^(1/2)=8/sqrt(5)=(8/5)sqrt(5)}}}
{{{sqrt(5)*(25/16)^(3/4)=sqrt(5)*(5sqrt(5))/8=25/8}}}
So then,
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))=5sqrt(5)+(8/5)sqrt(5)+25/8)}}}
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))=(25/5+8/5)sqrt(5)+25/8)}}}
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))= (33/5)sqrt(5)+(25/8) }}}
and 
{{{2/(sqrt(5)+2)=(2/(2+sqrt(5)))*((2-sqrt(5))/(2-sqrt(5)))}}}
{{{2/(sqrt(5)+2)=(4-2sqrt(5))/(4-5)}}}
{{{2/(sqrt(5)+2)=(4-2sqrt(5))/(-1)}}}
{{{2/(sqrt(5)+2)=2sqrt(5)-4}}}
So then multiplying,
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))*(2/(sqrt(5)+2))=(33/5)sqrt(5)+(25/8)(2sqrt(5)-4)}}}
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))*(2/(sqrt(5)+2))=(33/5)*2*5-(33/5)*4*sqrt(5)+(25/8)*2*sqrt(5)-(25/8)4}}}
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))*(2/(sqrt(5)+2))=66-(132/5)sqrt(5)-(25/4)sqrt(5)+25/2}}}

{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))*(2/(sqrt(5)+2))=(132/2+25/2)-sqrt(5)(132/5+25/4)}}}
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))*(2/(sqrt(5)+2))=(157/2)-sqrt(5)(528/20+125/20)}}}
{{{(125^(1/2)+(5/64)^(-1/2)-sqrt(5)*(25/16)^(3/4))*(2/(sqrt(5)+2))=(157/2)-sqrt(5)(653/20)}}}
So then,
{{{157/2=(2/5)m}}}
{{{m=785/4}}}
and
{{{(2/5)n=-653/20}}}
{{{n=-653/8}}}