If you have a PDF file and want it to be in a specific PDF version (for example, the print shop where you just ordered some adhesive labels wants the print master in PDF 1.3, but your Inkscape only exports PDF 1.4), Ghostscript can help:

gs -sDEVICE=pdfwrite -dCompatibilityLevel=1.5 -dNOPAUSE -dQUIET \
  -dBATCH -sOutputFile=new-pdf1.5.pdf original.pdf

(this converts the file original.pdf to PDF 1.5 and writes it to new-pdf1.5.pdf)

Also, if you have a huge PDF of several megabyte because there are many high-resolution pictures in it, Ghostscript can minify it (and shrink the pictures to 96 dpi) if you use the parameter -dPDFSETTINGS=/screen.