I need to speed up the connection between 2 machines on my small
network, they both have Gigbit NIC but are connected via the inbuilt
100Mb/s switch in my ADSL router so thoughput is limited.

So I'm going to get a gigabit switch and connect the 2 via the cat5e
cabling I've already got.

Now I've got conflicting information about how likely this is to work,
some say you definately need cat6, some say cat5e is fine whatever and
other say cat5e is ok for only very short cabling.

As I only need about 10m on one cable and 3m on another am I likely to
be able to get away with my current cat5e?

I ask because the only 2 local suppliers of cat6 charge a small fortune
for it (unless you buy a whole drum of it).