Is there a minimum length for a CAT5 patch cable?
There is a minimum length defined only for 100BaseT Ethernet networks (which is 2,5 meters) and this also includes the patch cable which is used to allow us to connect the end of a wired segment from patch panel of a communications rack into a switch or hub.
Because of the way all networks are setup and wired, the total segment length (including the patch cable) is always well over 2,5 meters, this is also the reason why the minimum cable length in such networks is never an issue.
If you are using CAT 5 patch cables on a 10BaseT network there is no minimum length in the Ethernet specification.
Just keep in mind that need to ensure that the total length of any 10 or 100 BaseT segment, starting from the PC its connected to, all the way to the patch panel and the patch cable you will be using, does not exceed 100 meters.
It's quite rare you will ever find yourself exceeding the limit, and if you do, then you simply need to add a repeater before the 100 meter limit so it can reconstruct the signal and send it out again.
There are also a few guidelines, which should be followed in such situations, and if you like to learn about them, please check my past answers where I have mentioned them.