Determine the big$-$O notation for the following: $5n^{\frac{5}{2}}+n^{\frac{2}{5}}$

$O(n^{\frac{5}{2}}+n^{\frac{2}{5}})=O(n^{\frac{29}{10}})$

$O(n^{\frac{2}{5}})$

$O(n^{\frac{10}{10}})=O(n)$

$O(n^{\frac{5}{2}})$