Finding the Reduced Form Equations

Hey this is my first post here. I'm doing a regress with 5 equations and 5 endogenous vairables plus one unique exogenous variable to each equation. As such my system is just identified and I need to find the reduced form equations inorder to receive an unbiased estimate of the coefficients. Basicaly this amounts to solving a 5x5 linear equation with variable coefficients. I started doing this on paper but realized it would take me hours and I would likely mess it up. Is there any easy way (math trick or computer program) that will make this easier for me? Thanks alot for any help yall can give.