back at it again (this time in an image)

Call the intersection of PR and SQ  = O

Triangle SOR  similar to triangle YOX

XY / SR =  5 / 28

Then the height of triangle YOX is 5/28  of the height of triangle SOR

Then we can divide half of the height of the trapezoid into  33 equal parts

Height of  triangle SOR  is 28 of these parts and  height of triangle YOX is 5 of them

And triangle QOP  is similar to triangle SOR

So.....the height of triangle  QOP  =  33 + 5 =  38 equal parts of the total height of the  trapezoid

So, since the trangles are similar →    PQ  / SR  =   38 / 28

So PQ = (38/28) SR  =  (38/28) *  28  =   38