Short answer: Use a embedded data field with as a counter. So after a recipient sees a block the counter goes up one.
Long answer: You create a randomizer in the survey flow and present 8 items making sure not to repeat. Within the randomizer you have 22 groups that contain your block, a counter, your "like more?" block, and end/rest of survey. After ever one of those 22 blocks you update the counter by one and check it's value. If it equals 5 you ask the See More? block and if they say No you exit/continue with the rest of the survey.

MSobotta - Thank you! This is helpful. For the counter, can I simply start by defining embedded data as "counter=0" and then in future embedded data flow updates say "counter=counter+1" and have that work? Or do I have to use JavaScript (or something else... piped fields, etc.) in the embedded data updates after each block? (Hopefully my question makes sense... I'm still figuring this stuff out.)

I figured it out - and the answer is in this thread, for anyone who would like to know later:
https://community.qualtrics.com/XMcommunity/discussion/7088/hi-i-want-to-give-a-number-for-each-question-when-randomizing-block

I would not use js it's just not necessary.