+---+-------+---+
| 1 |   2   |   |
+---+---+---| 3 |  
|   4   | 5 |   |
+-------+---+---+

Vera,one of the performers in a play,was murdered in her dressing room. The following facts refers to the dressing rooms shown above. Each of the five performers in the play - Vera, Adam, Babe, Clay and Dawn - had his or her own dressing room.

1. The killer's dressing room and Vera's dressing room border on the same number of rooms.
2. Vera's dressing room borders on Adam's dressing room and on Babe's dressing room.
3. Clay's dressing room and Dawn's dressing room are the same size.
4. Babe's dressing room does not border on Clay's dressing room.
5. The five rooms come in precisely two distinct sizes. (For example, rooms 2, 3 and 4 have the same size.)

Who killed Vera?