ImportError: No module named 'tensorflow.core'

This is probably a bug in tensorflow. In 1.13, we have an __init__.py that contains:

__all__ = [_s for _s in dir() if not _s.startswith('_')]

# ... later ...
try:                                                                                                                                                                       
  del python
  del core

So while we remove python and core from the module, we do not remove them from __all__. This prevents use cases like from tensorflow import *. This should be fixed in Tensorflow 1.14 with this change.

The problem may be with packages installation directories like some packages are installed in home and some in /usr/. I suggest you to remove all the packages in home directory by finding them in ~/.local/lib/python3.5/site-packages and reinstall then with super user privileges.