In a 5000 gallon pool, 8-oz.of stabilizer should add about 13ppm of CYA to the water. So, that plus your current reading of 25 should take it up to 38. (It will take up to a week for the CYA to dissolve in the filter and show up on the test so don't retest for it or backwash for about a week.) The dichlor shock you are using also adds CYA. So, if you continue to use that, your CYA may get way too high before long. Go ahead and use another bag or two, but when you re-check the CYA in about a week, post the CYA reading. At that time, depending on your CYA level, you may need to stop using dichlor and switch to something else.

Your pH and alk are fine. Calcium is not needed in a vinyl pool, but some is ok. When it gets too high, it can cause cloudy water issues. It really would be best to stick with liquid pool store chlorine or just bleach.

Some pools open to a high chlorine demand that eventually goes away. Your pool may be one of them. It is caused by a breakdown of the CYA to ammonia and it takes a lot of chlorine to rid the pool of the ammonia. (Do you know what the CYA level was upon closing last fall?) Test the pool a few times each day, minimum of twice and more often than that is even better and will get you through this faster. Each time, shock the pool up to about 15ppm. When you get to the point where you can test it in the evening and not lose more than 1ppm of chlorine overnight from sundown to sunup the next day, then you should keep the high chlorine level for one additional day and then let it drift down. Once you report your CYA level in a week, we'll let you know what level that will need to be. (Chlorine levels are dependent on CYA levels. See the Best Guess table in my signature below.) To help you know how much bleach to add each time you test, in your pool, each quart of 6% bleach will add about 3ppm of chlorine.

Keep an eye on your pH. You are ok at 7.3 but don't let it drop below 7.0.

Hope this helps!