No, you need a Non-Cardbus card for it to work on your 5300 (I face the same problem on my 1400c/166 and 1400c/133 - No Ethernet jacks, which is a shame really).
No you cant, Cardbus was phased in in around 1997, this is the problem with running very old Macs (My solution was to hook my 1400s up to my PowerMac 8200/120, which has an Ethernet Jack. (This solution is obviously a complex solution to a simple problem, but since I had the 8200 kicking around it was cheaper than trying to find the correct card in eBay).