Hugo, Evo, and Fidel are playing Dungeons and Dragons, which requires many twenty-sided dice. Attempting to slay Evo's [i]vicious hobgoblin +1 of viciousness,[/i] Hugo rolls $25$ $20$-sided dice, obtaining a sum of (alas!) only $70$. Trying to console him, Fidel notes that, given that sum, the product of the numbers was as large as possible. How many $2$s did Hugo roll?
1. **Understanding the Problem:**
   Hugo rolls 25 twenty-sided dice, and the sum of the numbers rolled is 70. We need to determine how many 2's Hugo rolled if the product of the numbers is maximized.

2. **Formulating the Problem:**
   Let \( x_1, x_2, \ldots, x_{25} \) be the numbers rolled on the 25 dice. We know:
   \[
   x_1 + x_2 + \cdots + x_{25} = 70
   \]
   We need to maximize the product:
   \[
   P = x_1 \cdot x_2 \cdot \cdots \cdot x_{25}
   \]

3. **Using the Arithmetic Mean-Geometric Mean Inequality (AM-GM Inequality):**
   The AM-GM Inequality states that for non-negative real numbers \( a_1, a_2, \ldots, a_n \):
   \[
   \frac{a_1 + a_2 + \cdots + a_n}{n} \geq \sqrt[n]{a_1 \cdot a_2 \cdot \cdots \cdot a_n}
   \]
   Equality holds if and only if \( a_1 = a_2 = \cdots = a_n \).

4. **Applying AM-GM Inequality:**
   For our problem, we have:
   \[
   \frac{x_1 + x_2 + \cdots + x_{25}}{25} = \frac{70}{25} = 2.8
   \]
   Therefore:
   \[
   \sqrt[25]{x_1 \cdot x_2 \cdot \cdots \cdot x_{25}} \leq 2.8
   \]
   To maximize the product \( P \), the numbers \( x_1, x_2, \ldots, x_{25} \) should be as close to 2.8 as possible.

5. **Finding the Closest Integers:**
   The closest integers to 2.8 are 2 and 3. We need to find a combination of 2's and 3's that sum to 70.

6. **Setting Up the Equation:**
   Let \( a \) be the number of 2's and \( b \) be the number of 3's. We have:
   \[
   a + b = 25
   \]
   \[
   2a + 3b = 70
   \]

7. **Solving the System of Equations:**
   From the first equation:
   \[
   b = 25 - a
   \]
   Substitute into the second equation:
   \[
   2a + 3(25 - a) = 70
   \]
   \[
   2a + 75 - 3a = 70
   \]
   \[
   -a + 75 = 70
   \]
   \[
   -a = -5
   \]
   \[
   a = 5
   \]

8. **Conclusion:**
   Hugo rolled 5 twos and the remaining \( 25 - 5 = 20 \) threes.

The final answer is \( \boxed{5} \).