$\frac{59-x}{41}$+$\frac{57-x}{43}$+$\frac{55-x}{45}$+$\frac{53-x}{47}$+$\frac{51-x}{49}$=-5
\Rightarrow($\frac{59-x}{41}$+1)+($\frac{57-x}{43}$+1)+($\frac{55-x}{45}$+1)+($\frac{53-x}{47}$+1)+($\frac{51-x}{49}$+1)=0
\Rightarrow $\frac{100-x}{41}$+$\frac{100-x}{43}$+$\frac{100-x}{45}$+$\frac{100-x}{47}$+$\frac{100-x}{49}$=0
\Rightarrow (100-x)( $\frac{1}{41}$+$\frac{1}{43}$+$\frac{1}{45}$+ $\frac{1}{47}$+ $\frac{1}{49}$)=0
\Rightarrow x=100 (do$\frac{1}{41}$+$\frac{1}{43}$+$\frac{1}{45}$+ $\frac{1}{47}$+ $\frac{1}{49}$ >0)