Pour 5 cups of water into the pot, season with more salt and bring to a simmer. Cook, stirring occasionally, until the potatoes are very soft and nearly falling apart, 25 to 30 minutes. Use the spoon to mash down a few of the potatoes to help them release their starch, which will thicken the soup and make it even more creamy. Throw in the Swiss chard and simmer until just wilted, 2 to 3 minutes. Taste and add more salt, if needed.