To find the total length that Sven swims, we first need to calculate the total distance he swims in yards.
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The length of the pool is \( 11 \frac{1}{3} \) yards. We can convert this mixed number into an improper fraction: \[ 11 \frac{1}{3} = \frac{11 \times 3 + 1}{3} = \frac{33 + 1}{3} = \frac{34}{3} \text{ yards.} \]
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Since Sven swims 5 laps, we multiply the length of one lap by 5: \[ \text{Total length} = 5 \times \frac{34}{3} = \frac{170}{3} \text{ yards.} \]
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Next, we convert \( \frac{170}{3} \) to a mixed number. We divide 170 by 3: \[ 170 \div 3 = 56 \text{ remainder } 2. \] This means that: \[ 170 = 3 \times 56 + 2. \]
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Therefore, we can write \( \frac{170}{3} \) as a mixed number: \[ \frac{170}{3} = 56 \frac{2}{3}. \]
Thus, the total length that Sven swims is \( \boxed{56 \frac{2}{3}} \) yards.
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