  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
from two crystallographic inequivalent Co1 and Co2 atoms. 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. These two types of atoms develop unequal net magnetic moments, a
feature that due to alternating sequence of Co1 and Co2 atoms gives rise to
antiferromagnetic component along crystallographic $c$-direction.
Antiferromagnetic component, initially small, drastically increases with
applied pressure, until Co2 atoms become nonmagnetic. Our density functional
theory results, supported by the analysis of a toy model for the found
orbital-selective ferromagnetic order, are consistent with the recently
reported resistivity measurements on La$_5$Co$_2$Ge$_3$ suggesting the presence
of a partially gapped magnetic phase under pressure. Although, proposed here
origin of antiferromagnetic component in La$_5$Co$_2$Ge$_3$ is an alternative
one to the advocated for this material ferromagnetic quantum criticality
avoidance, our findings indicate that the effects of the quantum fluctuations
can still play a key role at pressure larger than up-to-date measured 5GPa.
