Add HDF5 Section to read/write docs page (#8012)

* add HDF5 section to read/write docs

* change wording for hdf5 vs. netcdf4

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* add write section for hdf5 docs

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tom Nicholas <[email protected]>

doc/user-guide/io.rst

@@ -559,6 +559,67 @@ and currently raises a warning unless ``invalid_netcdf=True`` is set:
   Note that this produces a file that is likely to be not readable by other netCDF
   libraries!
 
+.. _io.hdf5:
+
+HDF5
+----
+`HDF5`_ is both a file format and a data model for storing information. HDF5 stores
+data hierarchically, using groups to create a nested structure. HDF5 is a more
+general verion of the netCDF4 data model, so the nested structure is one of many
+similarities between the two data formats.
+
+Reading HDF5 files in xarray requires the ``h5netcdf`` engine, which can be installed
+with ``conda install h5netcdf``. Once installed we can use xarray to open HDF5 files:
+
+.. code:: python
+
+    xr.open_dataset("/path/to/my/file.h5")
+
+The similarities between HDF5 and netCDF4 mean that HDF5 data can be written with the
+same :py:meth:`Dataset.to_netcdf` method as used for netCDF4 data:
+
+.. ipython:: python
+
+    ds = xr.Dataset(
+        {"foo": (("x", "y"), np.random.rand(4, 5))},
+        coords={
+            "x": [10, 20, 30, 40],
+            "y": pd.date_range("2000-01-01", periods=5),
+            "z": ("x", list("abcd")),
+        },
+    )
+
+    ds.to_netcdf("saved_on_disk.h5")
+
+Groups
+~~~~~~
+
+If you have multiple or highly nested groups, xarray by default may not read the group
+that you want. A particular group of an HDF5 file can be specified using the ``group``
+argument:
+
+.. code:: python
+
+    xr.open_dataset("/path/to/my/file.h5", group="/my/group")
+
+While xarray cannot interrogate an HDF5 file to determine which groups are available,
+the HDF5 Python reader `h5py`_ can be used instead.
+
+Natively the xarray data structures can only handle one level of nesting, organized as
+DataArrays inside of Datasets. If your HDF5 file has additional levels of hierarchy you
+can only access one group and a time and will need to specify group names.
+
+.. note::
+
+    For native handling of multiple HDF5 groups with xarray, including I/O, you might be
+    interested in the experimental
+    `xarray-datatree <https://github.com/xarray-contrib/datatree>`_ package.
+
+
+.. _HDF5: https://hdfgroup.github.io/hdf5/index.html
+.. _h5py: https://www.h5py.org/
+
+
 .. _io.zarr:
 
 Zarr