Export 5D image sequence in tif (and HDF5) formats

I'm looking for a way to export 5D image sequences in the tif and HDF5 formats. Sequences are made of RGB images and contain depth and time information. For example a movie contains 10 time frames and in each time frame there are 5 "slices" in depth, for a total of 50 images. For now the best I can do is export individual stacks on their own, but not as a single file containing everything which could be opened with ImageJ for example. In other words, I get 10 image sequences of 5 images each whereas I would like one single file containing the 50 images in the right order. Is there a clever way to do this? In a near future I would also like to export in the HDF5 format; would the method be pretty much similar? Thanks a lot.

Here is the code I'm using for exporting individual stacks:

[fileName,pathName] = uiputfile({'*.tiff'},'Select the folder in which to save the files');

  MovieToExport = zeros(ImageHeight,ImageWidth,3,TotalZSliceNumber,TotalTFrameNumber);     % The sequence is a 5D matrix containing RGB images, hence the 3 as the 3rd dimension.

        [~,~,ext] = fileparts(fileName);

        cd(pathName);

        MovieToExport = uint16(MovieToExport);

        % remove .tiff, otherwise the name of the file is incorrect
        fileName = regexprep(fileName,'\.tiff','');

  
        for i= 1:TotalTFrameNumber   % i.e. number of T frames...10 in my example above. 

   ExportedName = sprintf('%s%d.tif',fileName,i);

    for k =1:TotalZSliceNumber % number of individual planes in each stack

              MovieToExport(:,:,:,k,i) = MovieMatrix{i,k}; % MovieMatrix is a cell            array containing the image sequence.
                                                   
          imwrite(MovieToExport(:,:,:,k,i),ExportedName,'tif','WriteMode', 'append', 'Compression','none');                                               
          
      end

  end