It can be stressful when your pets get sick and you don't know what to do. The best thing to do is always provide the right environment which takes some research before getting them. We all have made mistakes in the past when it comes to animals but we are all here to help you save your remaining axolotls.
5 in a 10 gallon would have produced too much ammonia too fast. Has it been more than a day since you added them? The only axolotl I ever lost was one that was 1.5" and was moved to a 2.5gallon by itself due to too much size difference. I had to suddenly fly home to help my mom move and was gone 3 days. My gf fed all my axolotls on the second day but it had already died due to ammonia rising.
Ammonia burns their skin and gills and is super stressful and deadly if not removed. In a cycled tank you have bacteria that grow over all the surfaces (and inside the filter) that convert ammonia into nitrite.
Nitrite is just as bad as ammonia and requires another type of bacteria to convert it into nitrate.
Nitrates are the least harmful and can be tolerated if kept below 40ppm. They sit in your tank until you perform a water change to remove them. A test kit is important because your water changes rely on knowing how much needs to be changed to keep nitrates down. For example, a 10 gallon that has 40ppm nitrates needs at least a 50% water change to bring that to 20ppm. Usually its a 20-30% water change each week with a larger one a month.
Ammonia/nitrite should always be at 0 if you don't want a stressed axolotl. Any amount of ammonia or nitrite requires a water change large enough to bring it down to at most 0.25ppm.
When you add water to the tank you need to dechlorinate it, since tap water contains chlorine/chloramines as well as other heavy metals. practically all dechlorinaters remove these toxins as well. Adding too much untreated tap water will kill all the bacteria you need in you tank.
Establishing a cycled tank requires patience and close monitoring. Its best to do this without any pets in the tank. You need a test kit for this. Liquid test kits are the best and last for years.
first add an ammonia source, either pure ammonia or some food to get the ammonia over 1.0ppm
second keep monitoring until you notice the ammonia begins to go down. This can take a week or more. Make sure to always keep adding the ammonia source! When ammonia goes down nitrites should be going up which you should be checking for!
third After another week or more nitrites should be going down and the formation of nitrates should be present. Also ammonia should be reading 0.0ppm at this point. When nitrites read 0.0ppm and the only reading you get is nitrates,... congratulations! you cycled your tank!
You are waiting for two colonies of bacteria to form. Sometimes they colonize fast and sometimes it can take more than a month, but everyone has to do it otherwise they will be doing constant water changes.
Also if you have 2 axolols left you might want to think about going with a bigger tank. Its usually recommended to keep 1 adult in 10 gallons and 2 in 20g etc... You're creating more work if you overcrowd your tank (trust me I know about this) and unless you have time to keep up with maintenance, you will keep stressing the axolotls.