What is the best way to transfer money from the U.S. to Pakistan?

For US$ 5,000/month, your best option would be via Society for Worldwide Interbank Financial Telecommunication (SWIFT) (SWIFT) transfer. Alternatively, you can also open a bank account with UBL, HBL or NBP (in New York, all these 3 banks are licensed in NY) and do a direct transfer from there into Pakistan.