In recent years, there has been growing interest in alternative cycles to the standard 4-stroke Otto engine for improving efficiency and lowering emissions of spark-ignition engines. One proposed concept is the 5-stroke engine which uses two types of cylinders, a combustion cylinder and an expansion cylinder with a transfer port between them. Excess pressure in the combustion cylinder can be further expanded by using a second expansion cylinder to harness additional work. The expansion cylinder runs on a two-stroke cycle, allowing the use of two combustion cylinders to one expansion cylinder in a three cylinder configuration to increase efficiency. Previous work has investigated the performance of prototype 5-stroke engines compared to 1-D modeling results; none have conducted a thorough study on the interactions of various design parameters. In this paper, we explore the results of a 1-D parametric modeling study to examine the effect of various parameters such as bore, stroke, valve lift profiles, and compression ratio on engine brake thermal efficiencies of a three cylinder 5-stroke engine. Over the range of values examined our work indicates that an expansion cylinder bore to stoke ratio of 1.4 and expansion ratio 17.5 produces maximum brake thermal efficiency. The intake, transfer, and exhaust lift profiles have a strong effect on brake thermal efficiency with valve opening and closing points playing a key role. Additionally reducing the offset between the combustion and expansion cylinder improves the timing of the transfer process leading to improved brake thermal efficiency. Lastly the transfer volume between the combustion and expansion cylinder has minimal effect on the brake thermal efficiency.