The new peaks - Lhotse Middle, Lhotse Shar, Kanchenjunga South, Kanchenjunga Central and Kanchenjunga West - all measure over 8,400 metres (27,559 feet).
They will be opened to mountaineers once the move is approved by the International Mountaineering and Climbing Federation, officials said.
Nepal currently allows expeditions to scale eight mountains of over 8,000 metres, including Mount Everest, the world's tallest peak.
The International Mountaineering and Climbing Federation has already initiated the process to recognise the five peaks, said Ang Tshering Sherpa, senior vice-president of the International Mountaineers Association.
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"These peaks have already been opened for climbers by the Nepal government and we are just waiting for international recognition," he said.
"I believe strongly that the recognition of these peaks will bring in a new era of inspirational mountaineering campaigns in Nepal, which will bring new challenges to veteran climbers and light up the imaginations of the youth," Sherpa said.
Over 300 peaks are open to expeditions in Nepal, which collected Rs 35 million in mountaineering revenues during the spring season, officials said.