To convert the base 10 number $76575$ into base 5, we repeatedly divide the number by 5 and record the remainders.

Step-by-Step Conversion:

1. $76575 \div 5 = 15315$ remainder 0
2. $15315 \div 5 = 3063$ remainder 0
3. $3063 \div 5 = 612$ remainder 3
4. $612 \div 5 = 122$ remainder 2
5. $122 \div 5 = 24$ remainder 2
6. $24 \div 5 = 4$ remainder 4
7. $4 \div 5 = 0$ remainder 4

Now, reading the remainders from bottom to top, the base 5 representation of $76575$ is:

$\mathbf{4422300}_5$

Final Answer:

$76575_{10} = 4422300_5$

Would you like a deeper explanation or another example?

Related Questions:

1. How do you convert a number from base 5 to base 10?
2. What is the base 5 representation of 100,000 in base 10?
3. How can base 5 arithmetic be performed?
4. What is the largest 5-digit number in base 5, and what is its base 10 equivalent?
5. How do different bases impact computing and digital systems?

Tip:

When converting a number to another base, always write out the division steps carefully to avoid errors!