I think it's 5: you have to defend a lab while you try to get a transport full of units to another part of the island and destory a "hypno machine". I've tried every way I can think of; tried 7 times now, and get destroyed every time. What am I missing?

You could protect lab by using Platform (just move anyone unit, including Helicopter at the end of your turn into lab).

there is a tactical trick in this mission. You should withdraw your units so as to make the enemy advance through the desert (this will slow them down). Keep the lab occupied by your lighter units (you can unload some of the rocket laucnhers from platforms and move the latter into the lab). When the hypnotransmitter is destroyed the enemy bullfrogs will be frozen for several turns.

I've done the "withdraw" tactic from the first try. I also started using the copters and platforms in the base to keep them out from the second try on. When I destroy the hypno-machine, they stay frozen for one turn, and start attacking again

You shouldn't stay near opponent's units if can't destroy it. They can't move, but they can fire.

you can also move the Mortors off the platforms, then move the platforms ahead to block/slow down the advancing units. Also try moving some plafroms with rocketlaunchers out to sea where they can lob in rockets and stay out of the range of the bullfrogs and such. You might want to leave a tank back from the sea transport to protect the base. this will be needed later in the game.

You may look here... There is mission 5 of FNU Campaign replay.

I feel your pain, medium level - all day today with NO wins!!
I can get the hypo destroyed but lack resources to win the fighter part of it.

FNU-Hard another replay.Mission 5.There is one replay already,but i haven't ever plased replays so i want to try placing replays.

After seeing this mission, the campaign is more of a puzzle game than strategy game.

Hmm I played on medium. I finished of all of the attacking forces BEFORE i destroyed the hypnotransmitter. Using platforms and mortars to control the lab. After failing a few turns I found that it really was my two three opening moves that decided the whole battle. Save frontline units as long as possible and pound with artillery.

I finally finished this one. I messed up two times in a row by misjudging the distance the opponent could move when it captured the port.