Ensure you have anaconda 2021-05 installed (the latest standalone installer).
In Windows open up the Anaconda PowerShell Prompt or in Linux open up the Terminal.
Type in:
conda update --all
This should update the Anaconda Python distribution to the latest stable version, specifically updating Python to a compatible version for Spyder 5.
Next search the anaconda and conda-forge channels for the latest Spyder release:
conda search --channel anaconda spyder
conda search --channel conda-forge spyder
At the time of writing the conda-forge channel is more up to date than the anaconda channel.
Type in:
conda install --channel conda-forge spyder=5.0.3
On my Linux and Windows 10 install not specifying the version number preferenced spyder version 4.2.5