MPU6050 + arduino nano + raw data over serial

I've connected it to the I2C port (digital 4 and 5),

Then you've done it wrong, SDA is A4, SCL is A5 (not digital 4/5) and you must use 4.7k pull-up resistors on both those pins. If the device is 3.3V (which I believe it is) the pull-ups must go to +3.3V, not 5V.