Draw a parallelogram of diagonals 5cm and 7 cm and one angle as 60 degrees

We know that diagonals of parallelograms bisect each other.

Using this fact, we would draw two intersection lines with an included angle of 60° (and 120°).
From the intersection, measure out four vertices 5/2=2.5 cm on each side of one line, and 7/2=3.5 cm on each side of the other.
Join adjacent vertices to complete the required parallelogram.