Fiveash trained at the Adelaide School of Art and Design from 1881 to 1888 and later taught art privately and at Tormore House School in North Adelaide. She specialised in botanical drawing and in 1882 was commissioned by the conservator of forests in South Australia, John Ednie Brown, to illustrate his The forest flora of South Australia. The work was never completed, but Fiveash drew the sketches for 32 of the 45 lithographs that were included in the nine parts which were published between 1882 and 1890. Fiveash also illustrated scientific papers, including zoological and anthropological subjects. She is most well remembered for her longstanding collaboration with Dr. Richard Sanders Rogers, illustrating his publications on Australian orchids from the specimens he collected.

Fiveash was credited with introducing the art of china painting to South Australia. Around 1900 Fiveash spent two years overseas, but otherwise she lived her whole in the Fiveash family home in North Adelaide. Prior to her departure to England, the governor of South Australia, Lord Tennyson, and businessman Robert Barr Smith purchased a portfolio of Fiveash's work and donated it to state institutions so that her work would be preserved as part of the state's heritage. In 1937 Fiveash donated a collection of her work to the State Library of South Australia. She continued painting and sketching until a few years before her death when bad eye sight meant that she could no longer carry out the detailed work.