Export["test.h5", {{{1, 2}, {2, 3}}, {{10, 11}, {12, 13}}}, {"Datasets", {"m1", "m2"}}]
r = Import["test.h5", "Rules"]
Export["test1.h5", r, "Rules"]

Export::errelem: The Export element Dataset1 contains a malformed data structure and could not be exported to HDF5 format. >>
Export::noopen: Cannot open C:UsersajasjaDocumentstest1.h5. >>

Export["test.h5",
  {{{1,2},{2,3}},{{10,11},{12,13}}},
  {"Datasets",{"m1","m2"}},
  {"Attributes"->{
    "m1"->{
      "ScalarValue"->{10.0},
      "ArrayValues"->{1.0,2.0,3.0},
      "Info"->{""This is a text string""}},
    "m2"->{
      "ScalarValue"->{20.0},
      "ArrayValues"->{-1.0,-2.0,-3.0},
      "Info"->{""This is a text string""}}}}]

In[] := Import["example.h5", "Attributes"]
Out[] := {{ArrayValues->{1.,2.,3.},Info->{"This is a text string"},ScalarValue->{10.}},{ArrayValues->{-1.,-2.,-3.},Info->{"This is a text string"},ScalarValue->{20.}}}

In[1]:= Export["test.h5", "path/to/dataset" -> {
    "Data" -> {1, 2, 3, 4},
    "Attributes" -> {
      "DataDescription" -> "SomeIntegers",
      "DataLength" -> 4
      }
    }
  ];
Import["test.h5", {"Attributes", "path/to/dataset"}]

Out[2]= <|"DataDescription" -> "SomeIntegers", "DataLength" -> 4|>

In[3]:= Export["test.h5", {
   "Datasets" ->
    "path/to/dataset" -> {1, 2, 3, 4},
   "Attributes" ->
    "path/to/dataset" -> {
      "DataDescription" -> "SomeIntegers",
      "DataLength" -> 4
     }
   },
   "Rules"
];
Import["test.h5", {"Attributes", "path/to/dataset"}]

Out[4]= <|"DataDescription" -> "SomeIntegers", "DataLength" -> 4|>

In[5]:= Export["test.h5",
  "path/to/dataset" -> {
    "NewAttribute" -> <|"x" -> 1, "y" -> "z"|>
   },
  "Attributes",
  OverwriteTarget -> "Append"
];
Import["test.h5", {"Attributes", "path/to/dataset"}]

Out[6]= <|"DataDescription" -> "SomeIntegers", "DataLength" -> 4,
 "NewAttribute" -> <|"x" -> 1, "y" -> "z"|>|>

In[7]:= Export["test.h5",
  "path/to/dataset" -> {
    "DataDescription" -> "New description of the data."
   },
  "Attributes",
  OverwriteTarget -> "Append",
  "AppendMode" -> "Overwrite"
];
Import["test.h5", {"Attributes", "path/to/dataset"}]

Out[8]= <|"DataDescription" -> "New description of the data.", "DataLength" -> 4,
 "NewAttribute" -> <|"x" -> 1, "y" -> "z"|>|>