The number of atomic orbitals from the following having $5$ radial nodes is
$7\mathrm{s}, 7\mathrm{p}, 6\mathrm{s}, 8\mathrm{p}, 8\mathrm{d}$

The number of radial nodes for an orbital with principal quantum number $\mathrm{n}$ and azimuthal quantum number$\mathrm{l}$ is given by the expression:

Number of radial nodes $= \mathrm{n} - \mathrm{l} - 1$

Using this expression, we can determine the number of radial nodes for each of the given atomic orbitals:

$7\mathrm{s}:\mathrm{n}=7,\mathrm{l}=0 7-0-1=6$
$7\mathrm{p}:\mathrm{n}=7,\mathrm{l}=1 7-1-1=5$
$6\mathrm{s}:\mathrm{n}=6,\mathrm{l}=0 6-0-1=5$
$8\mathrm{p}:\mathrm{n}=8,\mathrm{l}=1 8-1-1=6$
$8\mathrm{d}:\mathrm{n}=8,\mathrm{l}=2 8-2-1=5$

Therefore, the atomic orbitals with $5$ radial nodes are $7\mathrm{p}, 6\mathrm{s}, \mathrm{and} 8\mathrm{d}$.