Alex,
There is a vast amount of information around about the A5 corrosion problem. The corrosion usually causes two 10k precision resistors to change their value. These set the voltage reference for the DAC that controls most of the operating points for the scope, including trigger levels (that causes the Test 5 failre) and also the brightness levels of trace and readout. There is a high probability that the screen will be OK after you replace the damaged components. Before I did my A5 repair I also had nothing visible on screen, I adjusted the Grid Bias pot before repairing the A5 board as a confidece measure to see that the rest of the scope was OK.
Roger