I have no recent experience with HDF5 files, however the h5write documentation for data indicates that it must be a numeric matrix or a MATLAB string array. Depending on what the structure contains, the struct2table (or struct2cell) functions would likely be required first, then table2array for a table.
That appears to me to be more involved than it should be, however that appears to be the only option.
And that only if the original structure and the data in it permits those conversions.
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