Step 1: Order the data.
Sorting the fifteen values gives \[ 5,6,7,8,8,9,10,11,12,14,14,14,15,15,17 \]
Step 2: Locate the median.
With $n=15$ the middle value is the $8^{th}$ term, since $(15+1)/2 = 8$. That term is $11$, so the median is $11$.
Step 3: Find the mode.
Counting repeats, $14$ appears three times while $8$ and $15$ appear twice each. The most frequent value is $14$, so the mode is $14$.
Step 4: Match the options.
Median is $11$ makes A true and C false. Mode is $14$ makes D true and B false.
Step 5: Answer.
\[ \boxed{A,\ D} \]