The base-nine representation of the number $N$ is $27{,}006{,}000{,}052_{\rm nine}$. What is the remainder when $N$ is divided by $5?$

$\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }3\qquad\textbf{(E) }4$
1. **Convert the base-nine number to its decimal (base-10) equivalent:**
   The given number in base-nine is \(27{,}006{,}000{,}052_{\text{nine}}\). To convert this to base-10, we use the formula for base conversion:
   \[
   N = 2 \cdot 9^{10} + 7 \cdot 9^9 + 0 \cdot 9^8 + 0 \cdot 9^7 + 6 \cdot 9^6 + 0 \cdot 9^5 + 0 \cdot 9^4 + 0 \cdot 9^3 + 0 \cdot 9^2 + 5 \cdot 9^1 + 2 \cdot 9^0
   \]

2. **Simplify the expression using modulo 5:**
   We need to find \(N \mod 5\). We can simplify each term modulo 5:
   \[
   9 \equiv -1 \pmod{5}
   \]
   Therefore:
   \[
   9^k \equiv (-1)^k \pmod{5}
   \]

3. **Apply the simplification to each term:**
   \[
   2 \cdot 9^{10} \equiv 2 \cdot (-1)^{10} \equiv 2 \cdot 1 \equiv 2 \pmod{5}
   \]
   \[
   7 \cdot 9^9 \equiv 7 \cdot (-1)^9 \equiv 7 \cdot (-1) \equiv -7 \equiv -2 \pmod{5}
   \]
   \[
   0 \cdot 9^8 \equiv 0 \pmod{5}
   \]
   \[
   0 \cdot 9^7 \equiv 0 \pmod{5}
   \]
   \[
   6 \cdot 9^6 \equiv 6 \cdot (-1)^6 \equiv 6 \cdot 1 \equiv 6 \equiv 1 \pmod{5}
   \]
   \[
   0 \cdot 9^5 \equiv 0 \pmod{5}
   \]
   \[
   0 \cdot 9^4 \equiv 0 \pmod{5}
   \]
   \[
   0 \cdot 9^3 \equiv 0 \pmod{5}
   \]
   \[
   0 \cdot 9^2 \equiv 0 \pmod{5}
   \]
   \[
   5 \cdot 9^1 \equiv 5 \cdot (-1) \equiv -5 \equiv 0 \pmod{5}
   \]
   \[
   2 \cdot 9^0 \equiv 2 \cdot 1 \equiv 2 \pmod{5}
   \]

4. **Sum the simplified terms:**
   \[
   N \equiv 2 + (-2) + 0 + 0 + 1 + 0 + 0 + 0 + 0 + 0 + 2 \pmod{5}
   \]
   \[
   N \equiv 2 - 2 + 1 + 2 \pmod{5}
   \]
   \[
   N \equiv 3 \pmod{5}
   \]

Therefore, the remainder when \(N\) is divided by 5 is \(\boxed{3}\).