To download pip on Windows, I followed https://pip.pypa.io/en/stable/installing/ (downloading the get-pip.py file, and then running it on Command Prompt).
However, I got
There is something blocking your installation. Try to add proxy and try it:
set HTTP_PROXY=http://<<username>>:<<password>>@<<proxy server>>:<<proxy_port>>
set HTTPS_PROXY=https://<<username>>:<<password>>@<<proxy server>>:<<proxy_port>>
You can upgrade to a newer version of Python to solve this.
So to answer your question: Yes, get a new version of python. According to the docs, you need python 2.7.9 or higher.
edit: I didn't see your version (2.7.5). So yes, it is a version issue. Updating python would solve it.
In my case, updating python version to 2.7.16 worked