I've spent hours for installing pygame, but it I didn't succeed.
I want a detailed installing instruction for pygame in python3.5 in Ubuntu16.04.
And I think it's a meaningful work for other people.
You probably do not have pip3.5 installed, so I believe you it's not been easy. So one solution may be to start installing pip3.5. Based on this article on how to install pip3 in Ubuntu, here's a possible solution for your problem.
First install setuptools for Python 3
sudo apt-get install python3-setuptools
Then install pip (which will include pip3.5):
sudo easy_install3 pip
After the previous two commands, you should have pip3.5 installed. Now you can simply do
sudo pip3.5 install pygame
I tried it on Ubuntu 16.04 and it worked.