In this study, we have investigated the existence and properties of solitons in an unmagnetized plasma composed of positive ions, negative ions, negatively charged dust grains, non-thermal electrons and non-extensive positrons. We have conducted our study on this complex plasma model because it moves away from simplistic and idealized plasma models. Also, study of solitons has not been conducted previously on this complex plasma model. Through the Sagdeev potential method we have derived the energy integral and investigated the variation of the Sagdeev potential for different values of the parameters that are involved in our plasma model. We have found that the non-thermal parameter (β) and the non-extensive parameter(q) significantly influence the features of the solitons. The features of the solitons are also found to be influenced by the Mach number (M), the negative ion to positive ion mass ratio (Ω), the positron to positive ion density ratio (δp) , the electron to positron temperature ratio (σp), the dust charge density ratio (δd ) and the negative ion to positive ion density ratio(δ_ ). The results from our study can be useful in investigating plasma in astrophysical environments, such as cometary tails and interstellar clouds.