We report on the observation of double transition - a first order and a second order transition in Gd5Si2-xCoxGe2 with x = 0, 0.1, 0.2 and 0.4 with the appearance of short-range ferromagnetic correlations. The first order phase transition is due to a combined magnetostructural transition from monoclinic paramagnetic phase to orthorhombic ferromagnetic phase on cooling while the second order transition arises from an orthorhombic paramagnetic to ferromagnetic phase on cooling. Structural studies show that the substituted compounds crystallize in a combination of Gd5Si2Ge2 and Gd5Si4 phases. Low-temperature X-ray diffraction measurements confirm the complete transformation from monoclinic to orthorhombic phase. DC magnetization measurements reveal an anomalous low field magnetic behaviour indicating a Griffiths-like phase. This unusual behaviour is attributed to the local disorder within the crystallographic structure indicating the presence of short-range magnetic correlations and ferromagnetic clustering, which is stabilized and enhanced by competing intra-layer and inter-layer magnetic interactions. The magnetostructural transition results in entropy changes (-ΔSM) of 9 J kg-1 K-1 at 260 K for x = 0.1, 8.5 J kg-1 K-1 at 245 K for x = 0.2 and 4.2 J kg-1 K-1 at 210 K for x = 0.4 for a field change of 50 kOe. Co substitution induces compelling crystallographic and magnetoresponsive effects in the Gd-Si-Ge system, which could be useful for potential and smart applications such as solid-state magnetic refrigeration and sensitive magnetic switching from paramagnetic to ferromagnetic state. Universal curve analysis has been carried out on the substituted samples to study the order of the magnetic transition.