OLED $2.59 https://m.aliexpress.com/s/item/32233342471.html
The rest is passive junk that's probably about 25¢.
That's more than $5, but this is what 120 seconds of searching on AliExpress turned up.
Software is where a lot of the value comes from. I assume it's using a clever hack like http://dmitry.gr/index.php?r=05.Projects&proj=11.%20Bluetoot...
like you said the passive components are pretty cheap, and you stay under 5$.
[1] https://www.aliexpress.com/item/EYEWINK-1pcs-lot-ATMEGA328P-... [2] https://www.aliexpress.com/item/LCD-Board-T420XW01-V2-06A39-... [3] https://www.aliexpress.com/item/Free-Shipping-Blue-0-96-inch...