CUDA install problem on Ubuntu 20.04 LTS + GPU

I am having difficulty getting TensorFlow 2.7.0 to work with GPU on Ubuntu 20.04.

The instructions at GPU support | TensorFlow do not describe the procedure for Ubuntu 20.04. Is that described anywhere?

When I run this test script:

import tensorflow as tf

print('TensorFlow version:',tf.__version__)
physical_devices = tf.config.list_physical_devices()
for dev in physical_devices:
    print(dev)

sys_details = tf.sysconfig.get_build_info()
cuda_version = sys_details["cuda_version"]
print("CUDA version:",cuda_version)
cudnn_version = sys_details["cudnn_version"]
print("CUDNN version:",cudnn_version)

I see:

$ python3 TensorFlow/test.py
TensorFlow version: 2.7.0
2021-11-29 17:30:21.825301: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libcudnn.so.8'; dlerror: libcudnn.so.8: cannot open shared object file: No such file or directory; LD_LIBRARY_PATH: :/usr/local/cuda-11.5/lib64:/usr/local/cuda-11.5/lib64
2021-11-29 17:30:21.825324: W tensorflow/core/common_runtime/gpu/gpu_device.cc:1850] Cannot dlopen some GPU libraries. Please make sure the missing libraries mentioned above are installed properly if you would like to use GPU. Follow the guide at https://www.tensorflow.org/install/gpu for how to download and setup the required libraries for your platform.
Skipping registering GPU devices...
PhysicalDevice(name='/physical_device:CPU:0', device_type='CPU')
CUDA version: 11.2
CUDNN version: 8

I have:

$ echo $LD_LIBRARY_PATH
:/usr/local/cuda-11.5/lib64:/usr/local/cuda-11.5/lib64

How might I fix the errors please?

@David_A, According to Tested build configuration CUDA: 11.2 and cuDNN:8.1 are compatible for TF2.7. Can you let us know the steps that you have followed to install GPU ?