By default you can never open models form newer version in older application. You should be getting message that part you're trying to open was created in newer release and cannot be retrieved. Also, if you created models in Creo Parametric using commercial license, you won't be able to open them at home using educational license (and you also should get explanation message). Every type of license allows only for loading models created with the same type of license, so you won't load models made with trial license into Creo with educational or commercial license and so on.
If Parametric was also using student license, then you need GCRI (Granite Cross Release Interoperability) - a set of libraries that allows loading newer models into older software and you can get them at http://www.ptc.com/products/granite/gcri/free-download.htm. In order to use them, you need to copy dll files from directory in Creo Parametric to \<loadpoint>\<architecture>\obj directory of Creo Elements/Pro 5.0 (eg. \<loadpoint>\i486_nt\obj for x86 installation) and add this options to config.pro for Pro 5.0:
topobus_enable yes
atb_show_log off
atb_auto_check_on_update off
atb_auto_check_on_retrieve on
Also, in Paramteric you need to set config.pro option cri_grafting_enable to yes (before launching Creo) and save desired model. Then you should be able to load it into Creo Elements/Pro.