To find out how many pounds of potatoes the restaurant bought, we start with the amount of onions purchased, which is 5 pounds. The restaurant bought \( 4 \frac{5}{6} \) times as much potatoes as onions.
First, we need to convert \( 4 \frac{5}{6} \) into an improper fraction:
\[ 4 \frac{5}{6} = 4 + \frac{5}{6} = \frac{4 \times 6}{6} + \frac{5}{6} = \frac{24}{6} + \frac{5}{6} = \frac{24 + 5}{6} = \frac{29}{6} \]
Next, we multiply this value by the weight of the onions:
\[ \text{Pounds of potatoes} = 5 \times \frac{29}{6} \]
To perform the multiplication, we convert the whole number 5 to a fraction:
\[ 5 = \frac{5}{1} \]
Now we can multiply:
\[ \frac{5}{1} \times \frac{29}{6} = \frac{5 \times 29}{1 \times 6} = \frac{145}{6} \]
Now, we can convert \( \frac{145}{6} \) into a mixed number. We divide 145 by 6:
145 divided by 6 equals 24 with a remainder of 1, so:
\[ \frac{145}{6} = 24 \frac{1}{6} \]
Thus, the restaurant bought
\[ \boxed{24 \frac{1}{6}} \text{ pounds of potatoes.} \]
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