If you have sudo rights, you can install HDF5 using your OS package manager, such as apt in the case of Debian-like distros:
sudo apt install libhdf5-dev hdf5-tools
Otherwise you need to build HDF5 from its sources, which you can download from here
Decompress them, then run the following commands:
If you want to specify where to install the software. Replace:
by
Where <install-path> is the absolute path to the directory where you want to install HDF5.