In the second month, Vinny lost half as much as he had the first month, so he lost 20 pounds / 2 = <<20/2=10>>10 pounds.
In the third month, he again lost half as much which was 10 pounds / 2 = <<10/2=5>>5 pounds.
And in the fourth month, he lost 5 pounds / 2 = <<5/2=2.5>>2.5 pounds.
So in total, Vinny lost 20 + 10 + 5 + 2.5 = <<20+10+5+2.5=37.5>>37.5 pounds in the first four months.
Over his entire diet, he had lost 300 – 250.5 = <<300-250.5=49.5>>49.5 pounds.
So in the fifth month, Vinny must have lost 49.5 pounds total loss – 37.5 pounds loss in the first four months = 12 pounds.
#### 12