The problem: to find the voltage at the node of R3, R4 and R5
Vs | | ,---+---, | | R1 R5 | | +--R4---+ | | R2 R3 | | '---+---' | gnd
Expressing it using conductances, I get
G1G4 + G5(G1+G2+G4) E=Vs---------------------------- (G1+G2+G4)(G3+G4+G5) - G4^2
And no, it's not homework. I'm long past that.