Best choice for use in a hydraulic arbor press is a "C" unit. You would need a 2-1/2 inch unit to run a 5mm x 20mm die:
Used machinery places, or even e-bay often turn those units up for pennies on the dollar vs new. Dies are available used, but you will probably find inch size stuff easier - 7/32 x 7/8 for instance.
Once you have the punch frame you can punch any size or shape you have dies for - that frame will punch a 1/8" round hole or a 1" square hole with the right die set.
This one is close to what you asked for 5.5mm x 25mm: