Two Indian soldiers were also killed in the incidents in Kupwara and Sopore areas early on Thursday.
Police say at least 60 militants have been killed by security forces in the disputed region in recent months.
Thousands of people have been killed in Kashmir since an anti-India uprising began in 1989.
Pakistan and India have overlapping territorial claims in Kashmir and have fought two wars over Kashmir.
The Indian army said four militants and a soldier have been killed in a a clash in Handwara area in Kupwara district.
Army sources told the BBC that the soldier had died in an "initial ambush" by the militants.
Earlier, another militant and a soldier were killed in a prolonged gun battle in the neighbouring town of Sopore, the army said.
The incidents came weeks after Pakistan called off high-level security talks after India refused to allow Pakistan's ambassador to meet separatist leaders from Kashmir.
In recent years violence has abated from its peak in the 1990s, but the causes of the insurgency are still far from resolved.
A ceasefire agreed in 2003 remains in place, but the nuclear-armed neighbours often accuse each other of violating it.

This article was about:
At least five suspected militants have been killed in two separate gun battles with security forces in Indian-administered Kashmir, authorities say.