According to Wikipedia, the phrase Big Five game was coined by white hunters and refers to the five most difficult animals in Africa to hunt on foot. They are the African elephant, Black rhinoceros, Cape buffalo, Lion and Leopard.

African elephant

African bush elephant (Loxodonta africana)

The African elephant (Loxodonta africana) is a very large herbivore having thick, almost hairless skin, a long, flexible, prehensile trunk, upper incisors forming long curved tusks of ivory, and large, fan-shaped ears. There are two distinct species of African elephant: African forest elephant (Loxodonta cyclotis) and the African bush elephant (Loxodonta africana). The elephants are difficult because despite their large size, they are able to hide in tall grass and are more likely to charge than the other species.[5]

Black rhinoceros

Black rhinoceros (Diceros bicornis)

The black rhinoceros (Diceros bicornis) is a large, thick-skinned herbivore having one or two upright horns on the nasal bridge. Rhinoceros may refer to either black or white rhinoceros. Among Big Five game hunters, the black rhinoceros is preferred.

Cape buffalo

African cape buffalo (Syncerus caffer)

The African or cape buffalo (Syncerus caffer) is a large horned bovid. Buffalo are sometimes reported to kill more people in Africa than any other animal, although the same claim is also made of hippos and crocodiles.[6] It is considered the most dangerous of the Big Five, reportedly causing the most hunter deaths,[7] with wounded animals reported to ambush and attack pursuers.[8]

Lion

Lion (Panthera leo)

The lion (Panthera leo) is a large carnivorous feline of Africa and northwest India, having a short, tawny coat, a tufted tail, and, in the male, a heavy mane around the neck and shoulders. Lions are desirable to hunters because of the very real danger involved. A lion may attack without provocation, and is considered by many to be the best of the Big Five.[9]

Leopard

Leopard (Panthera pardus)

The leopard (Panthera pardus) is a large, carnivorous feline having either tawny fur with dark rosette-like markings or black fur. Of the Big Five, it is most difficult to acquire hunting licenses for leopards. The leopard is sometimes considered the most difficult of the Big Five to hunt because of their nocturnal and secretive nature. They are wary of humans and will take flight in the face of danger. The leopard is solitary by nature, and is most active between sunset and sunrise, although it may hunt during the day in some areas. Leopards can be found in the savanna grasslands, brush land and forested areas in Africa.

Leopard hunting uses the same methods as hunting for lions. Baiting, hounding and stalking are the most common methods used today to hunt the cat.