To convert the base-5 number $124420_5$ to base-10, we need to expand it as follows:

$124420_5 = 1 \cdot 5^5 + 2 \cdot 5^4 + 4 \cdot 5^3 + 4 \cdot 5^2 + 2 \cdot 5^1 + 0 \cdot 5^0$

Now, calculating the powers of 5:

$5^5 = 3125, \quad 5^4 = 625, \quad 5^3 = 125, \quad 5^2 = 25, \quad 5^1 = 5, \quad 5^0 = 1$

Substitute these values into the expression:

$124420_5 = 1 \cdot 3125 + 2 \cdot 625 + 4 \cdot 125 + 4 \cdot 25 + 2 \cdot 5 + 0 \cdot 1$

$= 3125 + 1250 + 500 + 100 + 10 + 0$

Now, sum the terms:

$3125 + 1250 + 500 + 100 + 10 = 4985$

So, $124420_5 = 4985_{10}$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you convert a base-7 number to base-10?
2. Can you convert $32014_5$ to base-10?
3. What is $4985_{10}$ in base-5?
4. How do you convert base-10 numbers to any other base?
5. How does place value work in different numeral systems?

Tip: When converting between bases, always start with the highest power and work your way down.