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5e is minimal for Gigabit, but if you have this small a network and the lengths of the cables are under 100m, installed and terminated properly, and pass testing for Gig you should be OK. If you terminated the Cat5e to a standard 8 position modular jack (as called for in the standards) you will not need to change them either. If your 10/100 switches have a gigabit uplink port, you will be fine. If you can picture going from New York to California – your speed will not always be the same, but for the parts of the trip when you can move faster, well, you move faster. Just because you have to slow down once in a while does not mean that you should only drive the slower speed.
I don't know how many devices that you have on your network, but, check and find out how many of the D Link switches you can stack together and make sure that you don't exceed it. The smaller switches have less room for buffering and address tables, so if you over extend them, you will have one heck of a mess.
This was first published in March 2004