[entrepy123]

What kind of printer prints 3x5" (or larger) index cards well?

IME most printers struggle with printing thicker cardstock, or non-normal sizes, e.g. trouble with keeping that size paper straight or with bending/feeding.

Is it just a normal-sized printer, or are there special index-card printers?

[meganlanziello]

Brother HL-6200DW (or similar variation). Before that I used another brother printer. When I researched (noting this was years ago) that was the only one that it would work with (may be others now). I had tried on various HP printers but they didn't work. Now you have to be careful how many cards you stack in the manual hopper also it works but not super robust.