The five were caught from Cooch Behar and Falakata in West Bengal and Dhubri in Assam by BSF under Frontier Headquarters, Guwahati this week, they said.
They were allegedly involved in smuggling contraband and cattle across the international border.
The Bangladeshi nationals were identified as Deben Das, Deben Sen and Jewel Hussain.
BSF seized various contraband and 376 cattle besides Indian and Bangladeshi currencies.