A review into the dramatic incident found swages (clamps that join wire cables together) buckled, enabling lacing that connects the mesh fence to a tension cable to unravel.
The escapees were then able to create and squeeze through a gap.
"The lions played and interacted with the fence for approximately 20 minutes before four cubs, and later adult male Ato, were able to breach it," the facility said.
"Lioness Maya and one cub chose to remain in the exhibit."
Ato and the four other cubs explored the other side of the main containment fence, remaining within metres of their exhibit before trying to find their way back under the fence.
"While trying to find an access back into the exhibit, two of the cubs moved past a secondary fence within the zoo," the facility said.
"One cub made its own way back into the exhibit, while the other was safely tranquilised and later returned to the dens."
The lions remain in a back-of-house holding area while Taronga waits for specialist engineering advice.
If any repairs or reinforcements are needed, the zoo will need to seek approval from the NSW Department of Primary Industries before returning the lions to their main exhibit.
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