The army did not specify when the troops were killed, but Sudan has deployed hundreds of soldiers as part of the coalition that is fighting the rebels backed by Iran in a war which the United Nations says has already left around 7,700 people dead and 42,500 wounded.
Khartoum joined the Sunni coalition led by Saudi Arabia in 2015 after breaking decades-old ties with Tehran.
The Sudanese military has largely refrained from offering details of its operations within the coalition or of casualties it has suffered in the conflict so far.
"We have lost five martyrs including an officer, and 22 others have been wounded," army spokesman Brigadier Ahmed Khalifa al-Shami said in a statement.
Without offering details, he said Sudanese forces had completed yesterday their "first stage of duty" in Yemen and were now preparing to launch the second stage.
"Our troops in Yemen have captured all the areas targeted in the first stage, inflicted big losses on the enemy and are holding many prisoners of war," Khalifa said.
The Saudi-led coalition also comprises the Gulf monarchies Bahrain, Kuwait, Qatar and the United Arab Emirates along with Egypt, Jordan, Morocco and Sudan.
According to the UN, the fighting has displaced more than three million people, and more than two thirds of Yemen's population of around 18.8 million people need aid.
Some 7.3 million people are estimated to be close to starvation and 462,000 children suffer from serious malnutrition. Without $2.1 billion in international aid, the UN warns that Yemen will suffer a famine in 2017.
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