Honorary mention from Tashkent (Uzbekistan), indicating the direction to Karachi (Pakistan), Bandar Abbas (Iran), and Hamburg (Germany). Not a record holder because the distances are not indicated, but according to Openstreetmap, along the indicated routes, distances by road are:
- Tashkent - Samarkand - Termez - Mazari-Sharif - Kabul - Karachi: 3114 km
- Tashkent - Samarkand - Termez - Marari-Sharif - Herat - Bandar Abbas: 3547 km
- Tashkent - Samarkand - Bukhara - Ashgabad - Bandar Abbas: 3284 km
- Tashkent - Samarkand - Bukhara - Nukus - Astrakhan - Volgograd - Warsaw - Hamburg: 6264 km
Source: Doris Antony, CC-BY-SA 3.0, Wikimedia Commons
This - barely - exceeds the 5976 km from Пеледу́й to Moscow, but alas — no distances are actually indicated on this sign, which is why I consider it an honorary mention and not a real answer to the question. But I think it should be mentioned here, because unlike the typical novelty signs showing the direction from a central European town to Australia or Alaska, the drive from Tashkent to Hamburg is actually possible, and probably the safest of all the routes indicated on the sign (as long as Astrakhan - Warsaw avoids Donbass/eastern Ukraine).