Answer
$2.25$ and $7.41$
Work Step by Step
Step 1. Draw a diagram as shown in the figure.
Step 2. Use the Law of Cosines, the length of one diagonal is $D_1^2=5^2+3^2-2\times3\times5cos50^{\circ}$ which gives $D_1=2.25$
Step 3. Use the supplementary angle $180-50=130^{\circ}$, the length of the other diagonal is $D_2^2=5^2+3^2-2\times3\times5cos130^{\circ}$ which gives $D_2=7.41$
