  We present density functional theory calculations for low-$T_c$ metallic
ferromagnet La$_5$Co$_2$Ge$_3$ at ambient and applied pressures. Our
investigations reveal that the system is a quasi-one-dimensional ferromagnet
with a peculiar coexistence of two different orbital-selective magnetic moments
at two crystallographically inequivalent cobalt atoms, Co1 and Co2. Namely, due
to different crystal-field splitting, the magnetic moment of Co1 atoms
predominantly derives from $d_{xz}$ orbital whereas of Co2 atoms from $d_{xy}$
orbital. Consequently, Co1 and Co2 atoms develop unequal net magnetic moments,
a feature that gives rise to a periodic, spatial modulation of magnetization
along crystallographic $c$-direction. The amplitude of the spatial modulation,
small at ambient pressure, drastically increases with applied pressure, until
Co2 atoms become nonmagnetic. With the help of a toy model mimicking found
orbital-selective ferromagnetic order, we demonstrate that the increasing
amplitude of spatial modulation provides a consistent interpretation to the
recently observed resistivity anomaly emerging at applied pressure identified
as the appearance of the {\it new state}. Although, proposed here structural
origin of the spatial modulation of magnetic moments in La$_5$Co$_2$Ge$_3$ is
an alternative one to the advocated for this material ferromagnetic quantum
criticality avoidance, the effects of quantum fluctuations can still play an
important role at pressure larger than up-to-date measured 5GPa.
