I could sequentially read the data in the file, print it via serial port and reconstruct it on the PC side, but that seems awfully messy and difficult with different 5 machines.
Aren't the 5 machines writing to the same file in the SD card? If not, then, the fact that there are 5 machines writing to 5 separate files seems completely irrelevant. If so, the fact that there are 5 machines writing TO the file IS irrelevant, since there is only one reading FROM the file.
There must be a better way.
Why must there be? Using functions, to manage the (relatively mild) complexity of the task would help.
Unfortunately I know next to nothing about networking.
And yet you have 5 machines talking to the Arduino? Getting the Arduino to talk to one more (the PC) seems easy, by comparison.
I suspect that you are simply underestimating yourself.