Taking off with a 5kt tail wind is not ideal - but so long as all
the performance figures are good, then there is probably nothing preventing you
doing it.
In the scenario given, what is likely to be a problem is the 30kt wind at 300ft .... IF you take-off into the 5kt HEADWIND, then at
300ft you will suddenly pick up a 30kt TAILWIND as you fly through the
inversion - in other words you will see 30kts disappear from your IAS - control
could certainly be a problem!!
In this scenario, you must T/O with the tailwind.