To find the length of Kinsley's picture, we start by noting that the height is given as \( 4 \frac{1}{4} \) inches.
First, we convert \( 4 \frac{1}{4} \) into an improper fraction.
\[ 4 \frac{1}{4} = 4 + \frac{1}{4} = \frac{16}{4} + \frac{1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \]
Now, we know that the length of the picture is 5 times its height. Therefore, we can set up the equation for the length \( L \):
\[ L = 5 \times \text{height} \]
Substituting the height:
\[ L = 5 \times \frac{17}{4} \]
To calculate this, we multiply 5 by the fraction:
\[ L = \frac{5 \times 17}{4} = \frac{85}{4} \]
Next, we can convert \( \frac{85}{4} \) into a mixed number. We divide 85 by 4:
\[ 85 \div 4 = 21 \quad \text{with a remainder of} \quad 1 \]
Thus, we can express \( \frac{85}{4} \) as:
\[ 21 \frac{1}{4} \]
Thus, the length of Kinsley's picture is:
\[ \boxed{21 \frac{1}{4}} \text{ inches} \]
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