The problem asks to convert the number $43112_5$ (which is in base 5) to base 10.

We convert a base-5 number to base-10 by expanding it using powers of 5. Each digit is multiplied by 5 raised to the power of its position, starting from the right (which is position 0).

The number $43112_5$ can be expressed as: $4 \cdot 5^4 + 3 \cdot 5^3 + 1 \cdot 5^2 + 1 \cdot 5^1 + 2 \cdot 5^0$

Now let's calculate each term: $4 \cdot 5^4 = 4 \cdot 625 = 2500$ $3 \cdot 5^3 = 3 \cdot 125 = 375$ $1 \cdot 5^2 = 1 \cdot 25 = 25$ $1 \cdot 5^1 = 1 \cdot 5 = 5$ $2 \cdot 5^0 = 2 \cdot 1 = 2$

Adding them up: $2500 + 375 + 25 + 5 + 2 = 2907$

Thus, $43112_5$ in base 10 is $2907_{10}$.

Would you like a detailed explanation or have further questions?

Here are five related questions to deepen your understanding:

1. How would you convert a number from base 10 to base 5?
2. Can you convert the base-5 number $1234_5$ to base 10?
3. How does the conversion change if the number is in base 2 instead of base 5?
4. What is the largest digit allowed in base 5, and why?
5. How do we perform addition and subtraction directly in base 5?

Tip: Always start the conversion from the rightmost digit when converting from any base to base 10.