diff --git a/cmake/FindHDF5.cmake b/cmake/FindHDF5.cmake
index 399b1c9f13..3230336a7d 100644
--- a/cmake/FindHDF5.cmake
+++ b/cmake/FindHDF5.cmake
@@ -88,7 +88,15 @@ if(NOT HDF5_INCLUDE_DIR OR NOT HDF5_LIBRARY_DIR)
     mark_as_advanced(HDF5_DIR)
     if(HDF5_DIR)
         message(STATUS "HDF5: found config at '${HDF5_DIR}'.")
-        set(HDF5_LIBRARIES hdf5_cpp-static)
+        if(TARGET hdf5_cpp-static)
+            set(HDF5_LIBRARIES hdf5_cpp-static)
+        elseif(TARGET hdf5_cpp-shared)
+            set(HDF5_LIBRARIES hdf5_cpp-shared)
+        elseif(TARGET hdf5::hdf5_cpp-shared)
+            set(HDF5_LIBRARIES hdf5::hdf5_cpp-shared)
+        else()
+            find_package(HDF5 REQUIRED COMPONENTS CXX)
+        endif()
     else()
         # If it failed, still try to find as a module.
         # E.g. on Ubuntu `libhdf5-dev` doesn't provie hdf5-config.cmake.