To meet the constraints of your network, you can create dump files of smaller size, which will enable you to create dump files of 5 MB (or smaller than that).
exp user/pass FILE=D:P1.dmp,E:P2.dmp FILESIZE=5m LOG=splitdump.log
I have not tried the above syntax, but have tried this one, where a substitution variable is used, ensuring that you need not worry about how many dump files you have to specify beforehand. This will automatically generate as many dump files, as needed of requisite size
expdp user/pass tables=test directory=dp_dir dumpfile=dump%u.dmp filesize=5m