First, let's find out how much fertilizer is added to the storage container over the total time period.
The farm deposits 1.5 ft³ of fertilizer each week. After 5 weeks, the amount of fertilizer added is:
\[ 1.5 , \text{ft}^3/\text{week} \times 5 , \text{weeks} = 7.5 , \text{ft}^3 \]
So, after 5 weeks, the total amount of fertilizer in the container is:
\[ 7.5 , \text{ft}^3 \]
However, the problem states that there is already 15 ft³ of fertilizer in the container after 5 weeks. This indicates that there was already some fertilizer in the container before the 5 weeks started.
Next, let's determine how much more fertilizer is added in the next 14 weeks. In 14 weeks, the additional amount of fertilizer added will be:
\[ 1.5 , \text{ft}^3/\text{week} \times 14 , \text{weeks} = 21 , \text{ft}^3 \]
Now, we can calculate the total amount of fertilizer after the full 19 weeks (5 weeks + 14 weeks):
\[ 15 , \text{ft}^3 + 21 , \text{ft}^3 = 36 , \text{ft}^3 \]
Thus, the capacity of the storage container is:
\[ \boxed{36} , \text{ft}^3 \]
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