Let's break this problem down step by step:

Step 1: Convert A$2000 to Japanese Yen (¥)

The exchange rate is given as A$1 = ¥96.16. So, to convert A$2000 to Japanese Yen:

$\text{Amount in Yen} = 2000 \times 96.16 = ¥192,320$

Step 2: Calculate how much Yoshi spent

Yoshi spent ¥131,700 during his holiday.

Step 3: Calculate the remaining Yen

The remaining Yen is:

$\text{Remaining Yen} = 192,320 - 131,700 = ¥60,620$

Step 4: Round down the remaining Yen to a multiple of 1000

The remaining Yen (¥60,620) is rounded down to the nearest multiple of 1000, which is ¥60,000.

Step 5: Convert the remaining Yen back to Australian dollars

To convert the remaining ¥60,000 back to Australian dollars using the exchange rate of A$1 = ¥96.16:

$\text{Amount in Australian dollars} = \frac{60,000}{96.16} = 624.56$

Step 6: Round the result to the nearest multiple of 5 cents

Rounding A$624.56 down to the nearest multiple of 5 cents gives:

\text{Rounded amount} = A$623.95

Thus, Yoshi got back A$623.95.

Summary of Key Steps:

1. Convert initial A$2000 to ¥.
2. Subtract the spent Yen to find remaining Yen.
3. Round down the remaining Yen to the nearest 1000 Yen.
4. Convert the remaining Yen back to Australian dollars.
5. Round the result to the nearest 5 cents.

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If you'd like more details or have any questions, feel free to ask! Here are a few related questions for further exploration:

1. How do exchange rates affect international travel spending?
2. Why do currency exchange rates fluctuate between transactions?
3. How do you calculate the value of a currency exchange when the rate changes over time?
4. How is rounding down used in financial transactions?
5. Can you explain how exchange rate commissions or fees might affect the actual amount received?

Tip: Always be mindful of rounding conventions in financial transactions to ensure accuracy when dealing with real money!