Frenet Apparatus of the Curves and Some Special Curves in the Euclidean 5-Space $E^5$

In this study, initially the geometric meanings of the curvatures of the curves parametrized with the arc length are given in $E^5$. This is followed by the calculation of the Frenet vectors and curvatures of any curve. After these, some results have been given for the state of evolute curve $X$ being a W-curve and the Frenet vectors and curvatures of involute curve $Y$ have been calculated in terms of Frenet vectors and curvatures of the curve X. At last, the differential equation of the spherical curves, the equation of the radius and the center of the osculating hyperspheres have been achieved in $E^5$.