The Texel Mule cross was born on Thursday in Derbyshire and farm owner Mark Bayley said he was totally healthy.
The Bayley family nicknamed the young male Forrest in the hope his extra limb gives him the same love of running as film character Forrest Gump.
Bayley said although it was tempting to sell Forrest for meat, he would probably be kept as a family pet, the BBC reported.
The extra limb, which sits just behind Forrest's left front leg, is slightly shorter than the other four so is not interfering with his mobility at the farm in Ashbourne.
"It's a bit of a novelty for me and the children and their friends so it'll probably become a pet."
Other five-legged lambs have been reported in Northumberland, Wales and France over recent years.