This was a simple puzzle, and I got correct answers from many. These include Vishal Poddar, Pratik Poddar, Suman Saraf, Mahi Saraf and Anand Singhi. Well done all.
The answer is “Not Possible”. This is a simple application of graph theory. I am copying the answer directly from Vishal Poddar:
Lets consider 5 slots in each telephone. Every wire will occupy 2 slots.
Total slots 15*5=75.
Total wires require = 75/2 = 37.5 which is not an integer. Therefore not possible.
Hope you all enjoyed the puzzle!