The principal role of an LPG (Liquefied Petroleum Gas) unit is the separation of propane and butane from other products in a gas refinery. One of the other main products of the LPG unit is C-5(+) which is sold at the same price of crude oil after it is added into gas condensate. In this research, sixth refinery (Phases 15 and 16) of South Pars gas filed was selected as a case study example to find an efficient design for enriching the C-5(+) stream. Analysis of the C-5(+) stream exited from the LPG unit demonstrates that it contains more than 70 wt. % of valuable solvents such as pentane and hexane which are more expensive than crude oil. Therefore, the main goal of this research is to do calculations related to the separation of these solvents from the C-5(+) stream using the direct and indirect sequence of distillation columns. For this purpose, an optimum algorithm is recommended based on Fenske-Underwood-Gilliland (FUG) method in which design parameters (column pressure and reflux ratio) are optimized so that the objective function that represents the total annual cost (TAC) is minimized. Programming with MATLAB shows that the theory of the direct sequence of distillation columns is more economical than the indirect sequence (an annual income of 40,309,012$ is estimated with a fixed cost of 1,047,555 $). Economic calculations also revealed that the rate of return (ROR) and annual profit would be 38.48% and 650,000,000 $.year(-1), respectively, if the optimal direct sequences of distillation columns are performed in all the gas refineries of South Pars.