Car and gear shifter are shaking ?

It's about 2005 Mazda 3 Hatchback. When accelerating everything is normal. When keeping the same speed, everything is normal. When the speed goes bellow the current speed, then the car starts shaking. I decided to test it on open road to make sure it's not because of bumpy street. I accelerated up to 170km/h, while accelerating everything was normal. When I released the gas pedal the car and gearshift started shaking like crazy. When I wanted to put into 5th gear, the gearshift was shaking like crazy. It doesn't matter if the car is in netral, 1st, 2nd, 3rd, 4th or 5th. And it doesn't matter if the engine rpm is high or low. What could be the problem ?