Using HP paper with Epson inks may produce dubious results.
I rather suspect that the 5 x 7 paper is actually designed for or compatible with (and on the compatibility list for your printer's paper stock) ...your Epson printer.
As for colors being right on a camera's monitor but not on the computer... that is a matter of color profile (in the 1980s it might have been a matter of sheer incapacity to 'render' colors with complete accuracy, but that stage of imperfect equipment is long past and bygone.)
Color profiles are appropriate for printers, or for monitors. The *right* color profile is the one where the monitor colors match the printed-out colors, pretty much and in summary.
Also it depends upon whether you are viewing the pictures in an Adobe application. Adobe applications for graphic images and such, have their own peculiar tweaks, settings, and elaborations. If you want to see how your 'monitor' renders a picture, view the picture file in MS Paint
(All Programs - Accessories - Paint)
which has no color profile nor tweaks nor settings and will show you how Windows, alone, and its color profile, will render the image.
Epson inkjet ink isn't the same as Canon inkjet ink, and so they require papers appropriate for their chemical composition (including viscosity, drying time, and any binary change in colors upon drying, and several other aspects too.)
A cut-down sheet of the wrong paper will have the same problem. Esp. if it *is* the paper stock type and quality that is the problem.
This discussion can be continued later. Just come back to the page for your question (bookmark it if you like, that's a convenient way of making sure you rejoin the case.)
Billing is not something I have control over... but coming back to the same question will prevent additional charge for an additional question. Let's continue this question / discussion instead, on this page.