To solve for \( c \) in the equation
\[ \frac{2}{5}c + 5 = 95, \]
first, we will subtract 5 from both sides:
\[ \frac{2}{5}c = 95 - 5, \] \[ \frac{2}{5}c = 90. \]
Next, we will multiply both sides by \( \frac{5}{2} \) to isolate \( c \):
\[ c = 90 \times \frac{5}{2}. \]
Calculating this gives:
\[ c = 90 \cdot 2.5 = 225. \]
So the value of \( c \) is
\[ \boxed{225}. \]