To find the third term in the expansion of $(x + 5)^4$, we can use the Binomial Theorem. The Binomial Theorem states that:

$(a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k$

In this case, $a = x$, $b = 5$, and $n = 4$.

The general term (k-th term) in the expansion is given by:

$T_{k+1} = \binom{n}{k} a^{n-k} b^k$

For the third term ($k = 2$):

$T_3 = \binom{4}{2} x^{4-2} \cdot 5^2$

First, calculate the binomial coefficient:

$\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6$

Now, plug in the values:

$T_3 = 6 \cdot x^2 \cdot 25 = 150x^2$

However, the options provided do not match $150x^2$. There seems to be a discrepancy with the problem statement or options. Let me correct it.

Let's recalculate:

For the third term:

$T_3 = \binom{4}{2} \cdot x^{4-2} \cdot 5^2 = 6 \cdot x^2 \cdot 25 = 150x^2$

If the problem had a mistake in options, the correct coefficient would be 150x^2.

But if using different coefficients, we'd find the correct answer should be based on the corrected interpretation or problem. Given the process, none match perfectly. No provided option (a-d) matches this outcome.

You should verify the problem's coefficients or choices.