Answer:
Draw diagonal AC.
Set your calculator to degree mode.
Use the Law of Cosines to find AC.
AC = √(6^2 + 8^2 -2(6)(8)(cos 95°))
= 10.41
From this, use the Pythagorean Theorem to find DC.
DC = √(10.41^2 - 5^2) = 9.13
So the perimeter of ABCD is
5 + 6 + 8 + 9.13 = 28.13 cm