The Frontier Corps (FC) said the exchange of fire took place in the Kechh district of Balochistan province along the Iranian border, where militants had taken refuge in a house.
"One soldier embraced martyrdom while troops killed all five terrorists and recovered arms and ammunition," FC spokesman Murtaza Baig told AFP.
A bomb planted on a cycle exploded alongside a paramilitary patrol in Qalat district, some 160 kilometres (100 miles) south of the Balochistan capital Quetta, killing one soldier and wounding seven, the spokesman said.
Violence has surged this year in Balochistan, which borders Afghanistan and Iran. The province suffers from a separatist insurgency and Taliban militants.
In October, Amnesty International called on Pakistan to investigate the alleged torture and killing of more than 40 Baloch political leaders and activists against a backdrop of Pakistani military activities in the province.
Hundreds of people have died since rebels rose up in 2004 demanding political autonomy and a greater share of profits from the region's natural oil, gas and mineral resources.
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