First, we calculate the total cost of the shirts. If each shirt costs $5 and Desiree wants to order 200 shirts, the total cost is calculated as follows:
\[ \text{Total Cost} = \text{Number of Shirts} \times \text{Cost per Shirt} = 200 \times 5 = 1000 \]
Next, we know that Desiree has $350 in her savings. To find out how much more money she needs to raise, we subtract her savings from the total cost:
\[ \text{Amount to Raise} = \text{Total Cost} - \text{Savings} = 1000 - 350 = 650 \]
Thus, Desiree must raise $650 to pay for the cost of the shirts.