My best friend makes this every year for Easter. It is very a very simple recipe, but make sure you have a lot of time to finish it. I recommend starting it early the day before you will want to serve it.
Get 5 small bowls out to start. Mix 1 box of Jello with 1 cup boiling water and ½ cup cold water. Do this with all of the colors at the same time.
Heat the milk in a saucepan over low heat just until it reaches a lukewarm temperature. Meanwhile, in a large bowl, mix together 1 cup boiling water with the envelopes of plain gelatin. Whisk together until the gelatin is completely dissolved. Add the warm milk, sour cream, sugar and vanilla extract and whisk until thoroughly combined and completely smooth with no lumps.
Pour the first color into a 9x13-inch pan and refrigerate until set (about 45 minutes, but can vary depending on the temperature of your fridge and how full it is). Once it's set, very gently pour 1½ cups of the sour cream mixture on top. Return to the refrigerator for 45 minutes, or until set. Repeat with the colors and sour cream mixture until the last color is used (you will have some sour cream mixture leftover). When finished, refrigerate for at least another hour. Store in refrigerator until ready to serve; refrigerate leftovers.