In a word, no, you don't need to drain the pool. We can super chlorinate the pool, kill the algae and clean the water. But first you need to adjust a couple of the test readings to make the chlorine more efficient.
YourCYA (stabilizer) level is 5 ppm. It needs to be 35-40 ppm to get the water to hold a chlorine level. Until you get the stabilizer level up, it won't do much good to put chlorine in the pool because the sunlight will neutralize it.
The PH level needs to be lowered before you begin the process. An added benefit of this is it will bring the Total Alkalinity back in line.
To raise the stabilizer level to 40 ppm in a 10000 gal pool you need 47oz of dry stabilizer OR 118 oz of liquid stabilizer.
It takes time to add dry stabilizer to a pool. You have to take small amounts of stabilizer, 2 or 3 oz, make sure it is totally dissolved in a bucket of water and then add it to the pool. You can also put the whole 48 oz in a sock or stocking foot, tie it to a pole and hang it in front of the pool return until it dissolves. This will take 2 days or more.
With liquid stabilizer you can dilute the 118 oz in a 5 gal bucket of water and add it all at once. The drawback to liquid stabilizer is it is more expensive.
Backwash the filter before adding the stabilizer because once it's all added, you can't backwash for 48 hrs.
The PH needs to be dropped to 7.2 before this process is started. You do that with Muriatic acid. You can use either 31.45% or 14.5% Muriatic acid. Most pool supply stores carry it. Big box building supply stores carry it and most Janitorial supply stores carry it.
If you use 31.45% MA you will need 30 oz to drop the TA. If you use 14.5% MA you will need 60 oz. DO NOT smell the fumes when you open the container or when you are pouring the Muriatic acid.
Fill a 5 gal bucket about 3/4 full of water, measure out correct amount of acid for the strength you are using and slowly pour that into the water. Mix it a little and then slowly pour it into the pool in front of the return.
When that is done, get fresh chemical readings and we can start clearing it pool water.
In the meantime I need some additional information:
Do you have a FAS/DPD test kit? You really need one to do this.
What kind of filter do you have?
Do you already have shock on hand?
This process is easier when liquid chlorine is used.