The orange pentagon is an item used in The Eyes of Glouphrie and The Path of Glouphrie. It has a value of 10 in Oaknock's and Yewnock's machine, as calculated by multiplying the value of the shape's colour and the number of sides the shapes have:
Below is the value of each shape:
Colour
Value
Circle
Triangle
Square
Pentagon
Red
1
3
4
5
Orange
2
6
8
10
Yellow
3
9
12
15
Green
4
12
16
20
Blue
5
15
20
25
Indigo
6
18
24
30
Violet
7
21
28
35
Trivia
The orange pentagon is the only coloured shape that had no article in the item name ("a" or "an") prior to all the discs being renamed.