\( y=3 x^{5}-2 x^{4}+5 \sqrt{x}+3 \), at \( (0,5) \)

To solve for the value of the function \( y=3 x^{5}-2 x^{4}+5 \sqrt{x}+3 \) at the point \( (0,5) \), simply substitute \( x = 0 \) into the equation. This gives you \( y = 3(0)^{5} - 2(0)^{4} + 5\sqrt{0} + 3 = 0 - 0 + 0 + 3 = 3 \). Hence, at \( x = 0 \), the function evaluates to \( y = 3 \), which indicates that while the specified point on the graph is \( (0,5) \), the function value is actually \( (0,3) \). But don't let that confuse you! This kind of behavior where the graph doesn't match the expected coordinate is a common occurrence in mathematics, especially when dealing with polynomial and radical functions. It emphasizes the importance of analyzing how the function behaves around specific points. Always double-check with simple substitutions!