A few questions.

Are you still testing twice a day? When you add bleach, how high are you taking the chlorine? You need to be adding enough bleach to get to 20 each time you add it. You say that your chlorine level has never been below 5 since you started trying to clear this. Cl of 5 in a pool with a cya of 70 will never clear algae. You must SUSTAIN that high reading. If you can test and add more bleach three times a day that would be even better.

Since you are having some difficulty with the chlorine testing, do you have a reputable pool store that you can take a water sample to for testing? Let them run a complete set of numbers for you. Just don't let them talk you into buying a bunch of stuff while you are there.