Step 1: What we want.
An electron goes round the nucleus in circles called Bohr orbits. We compare how strongly it is pulled inward (its centripetal acceleration) in the 3rd orbit versus the 5th orbit.
Step 2: Meaning of centripetal acceleration.
For any object moving in a circle, the inward acceleration is
\[ a = \frac{v^2}{r} \]
where $v$ is its speed and $r$ is the radius of its circle.
Step 3: How speed and radius depend on the orbit.
In Bohr's model the speed gets smaller for higher orbits and the radius gets bigger:
\[ v \propto \frac{1}{n} \quad\text{and}\quad r \propto n^2 \]
Here $n$ is the orbit number.
Step 4: Build the rule for acceleration.
Put these into $a = v^2/r$:
\[ a \propto \frac{(1/n)^2}{n^2} = \frac{1}{n^4} \]
So acceleration falls very fast as $n$ grows. It is smaller for higher orbits.
Step 5: Make the ratio.
Since $a \propto 1/n^4$, the orbit with the smaller $n$ has the larger $a$:
\[ \frac{a_3}{a_5} = \frac{1/3^4}{1/5^4} = \left(\frac{5}{3}\right)^4 \]
Step 6: Work out the numbers.
$5^4 = 625$ and $3^4 = 81$. So
\[ \frac{a_3}{a_5} = \frac{625}{81} \]
The ratio is $625 : 81$, which is option (2).
\[ \boxed{a_3 : a_5 = 625 : 81} \]