The number of orbitals associated with quantum numbers $\mathrm{n}=5,\mathrm{}{\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}$ is:

For $\text{n=5}$  $\text{5s,}\text{5p,}\text{5d,}\text{5f}$ and $5\text{g}$ and subshell is available

In   $5\text{s}\to 1\text{orbital}$

$5\text{p}\to 3\text{orbital}$

$\text{5d}\to \text{5 orbital}$

$\text{5f}\to \text{7}\text{orbital}$

$5\text{g}\to \text{9}\text{orbital}$

In each subshell 1 electron of every orbital will belong to $m_5=+\frac{1}{2}$ So, Total number of orbitals that will be associate with  $m_5=+\frac{1}{2}$   will be $1+3+5+7+9=25$