\(\left[0,75\div5\%+\left(\frac{-1}{4}\right)^2-\frac{61}{6}\right]\cdot\frac{115}{116}\)
\(=\left[\frac{3}{4}\div\frac{1}{20}+\frac{1}{16}-\frac{61}{6}\right]\cdot\frac{115}{116}\)
\(=\left[15+\frac{1}{16}-\frac{61}{6}\right]\cdot\frac{115}{116}\)
\(=\frac{235}{48}\cdot\frac{115}{116}\)
\(=\frac{5\cdot47\cdot5\cdot23}{16\cdot3\cdot4\cdot29}=\frac{20725}{5568}\)