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In 1998, Michael Hirschhorn discovered the 5-dissection formulas of the Rogers-Ramanujan continued fraction $R\left(q\right)$ and its reciprocal. We obtain the 5-dissections for functions $R\left(q\right)R{\left(q^2\right)}^2$ and $R{\left(q\right)}^2/R\left(q^2\right)$, which are essentially Ramanujan’s parameter and its companion. Additionally, 5-dissections of the reciprocals of these two functions are derived. These 5-dissection formulas imply that the coefficients in their series expansions have periodic sign patterns with few exceptions.