Answer
Yes, no.
Work Step by Step
Check the length of each side:
Step 1. Length of the first side: $AB=\sqrt {(1-5)^2+(1-2)^2}=\sqrt {17}$
Step 2. Length of the 2nd side: $BC=\sqrt {(3-5)^2+(4-2)^2}=2\sqrt {2}$
Step 3. Length of the 3rd side: $CD=\sqrt {(3-(-1))^2+(4-3)^2}=\sqrt {17}$
Step 4. Length of the 4th side: $DA=\sqrt {(1-(-1))^2+(1-3)^2}=2\sqrt {2}$
Thus, it is a parallelogram. not a rhombus.
