The formula to calculate the radius of an orbit for a hydrogen-like atom/ion is:

$$ r_n = r_0 \frac{n^2}{Z} $$

where:

• $r_n$ is the radius of the nth orbit,
• $n$ is the principal quantum number (the orbit number),
• $r_0$ is the Bohr radius (radius of the first Bohr orbit in the hydrogen atom), and
• $Z$ is the atomic number (the number of protons in the nucleus).

We're dealing with a Li²⁺ ion and we're interested in the fifth orbit ($n = 5$), and given that $r_0$ is 0.51 Å and $Z$ for Li is 3, we can substitute these values into the formula:

$$ r_5 = 0.51 \times \frac{25}{3} \text{ Å} = 4.25 \text{ Å} $$

which is $4.25 \times 10^{-10}$ m, or equivalently $425 \times 10^{-12}$ m when converted to meters.