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

We need to find how many atomic orbitals from the list $$7s, 7p, 6s, 8p, 8d$$ have exactly 5 radial nodes. The number of radial nodes in an atomic orbital is given by

where $$n$$ is the principal quantum number and $$l$$ is the azimuthal quantum number.

For 7s: $$n = 7$$, $$l = 0$$, so radial nodes $$= 7 - 0 - 1 = 6$$.

For 7p: $$n = 7$$, $$l = 1$$, so radial nodes $$= 7 - 1 - 1 = 5$$. This one qualifies.

For 6s: $$n = 6$$, $$l = 0$$, so radial nodes $$= 6 - 0 - 1 = 5$$. This one qualifies.

For 8p: $$n = 8$$, $$l = 1$$, so radial nodes $$= 8 - 1 - 1 = 6$$.

For 8d: $$n = 8$$, $$l = 2$$, so radial nodes $$= 8 - 2 - 1 = 5$$. This one qualifies.

The orbitals with exactly 5 radial nodes are 7p, 6s, and 8d. Hence, the answer is $$3$$.