Let \( p \) represent the number of packages of pens Kaylee buys, and let \( q \) represent the number of packages of pencils she buys. Since each package of pens contains 5 pens, the total number of pens she buys is \( 5p \). Each package of pencils contains 11 pencils, so the total number of pencils is \( 11q \).
We want the number of pens to equal the number of pencils, which gives us the equation:
\[ 5p = 11q \]
To find the smallest number of pens that Kaylee can buy, we rearrange this equation to isolate one of the variables. We can express \( p \) in terms of \( q \):
\[ p = \frac{11q}{5} \]
For \( p \) to be an integer, \( 11q \) must be a multiple of 5. This indicates that \( q \) must be a multiple of 5, because 11 and 5 are coprime (they share no prime factors).
Let’s denote \( q \) as \( q = 5k \), where \( k \) is a non-negative integer. Substituting this into our equation, we have:
\[ p = \frac{11(5k)}{5} = 11k \]
Now, substituting \( p \) and \( q \) back into the equation for the total number of pens, we can express it in terms of \( k \):
\[ \text{Total number of pens} = 5p = 5(11k) = 55k \]
To find the smallest number of pens, we set \( k = 1 \):
\[ \text{Total number of pens} = 55 \times 1 = 55 \]
Thus, when \( k = 1 \), the number of packages of pencils will be:
\[ q = 5k = 5 \times 1 = 5 \]
Given \( q = 5 \), Kaylee will buy:
\[ \text{Total number of pencils} = 11q = 11 \times 5 = 55 \]
In conclusion, if she buys 55 pens and 55 pencils, the condition \( 5p = 11q \) holds. Therefore, the smallest number of pens that Kaylee can buy is
\[ \boxed{55} \]