How to update python 2.7.5 to python 2.7.15 on centos 7.4?

It is unwise and probably almost impossible to update the system version of python - so much depends on it and being python, it depends on that specific version. (If you try and do 'yum erase python' it won't do it because yum itself relies on that python version.)

You have two options really. Install another version of python somewhere else - but DO NOT make it the default version - or you can use Software Collections. The latter is really the correct and supported way of doing it - see

https://www.softwarecollections.org/

There is a python 2.7.13 in there

https://www.softwarecollections.org/en/scls/rhscl/python27/

if that is sufficient for you.

P.