For your first error:
ImportError: libcudart.so.8.0: cannot open shared object file: No such file or directory
Please make sure your LD_LIBRARY_PATH includes the lib64 directory in whichever path you installed the cuda package in. You can do this by adding the export line in the .bashrc.
I fixed this issue just adding the cuda path to my .bashrc as below:
I hope you have installed cuDNN? Note that this is very different from the regular cuda package. You will need to first register, then download and install the package from the below page: https://developer.nvidia.com/cudnn
For your Second error :
ImportError: libcudnn.5: cannot open shared object file: No such file or directory
I found that there is no libcudnn.5 in my /usr/local/cuda/lib64 or /usr/local/cuda-8.0/lib64 directories. But, I do have a libcudnn.so.6.* file. So to solve the issue, I created a following link:
ln -s libcudnn.so.6.* libcudnn.so.5
in my /usr/local/cuda/lib64 directory. Now everything works fine for me.
I hope it helps you in resolving your issue.