  $\text{La}_{5}\text{Co}_{2}\text{Ge}_{3}$ is an itinerant ferromagnet with a
Curie temperature, $T_C$, of $\sim$ 3.8 K and a remarkably small saturated
moment of 0.1 $\mu_{B}/\text{Co}$. Here we present the growth and
characterization of single crystals of the ${\text{La}_{5}\text{(Co}_{1-x}\text
{Ni}_{x})_2\text {Ge}_{3}}$ series for 0.00 $\leq x \leq$ 0.186. We measured
powder X-ray diffraction, composition as well as anisotropic temperature
dependent resistivity, temperature and field dependent magnetization along with
heat capacity on these single crystals. We also measured muon-spin
rotation/relaxation ($\mu \text{SR}$) for some Ni substitutions ($x$ = 0.027,
0.036, 0.074) to study the evolution of internal field with Ni substitution.
Using the measured data we infer a low temperature, transition
temperature-composition phase diagram for ${\text{La}_{5}\text{(Co}_{1-x}\text
{Ni}_{x})_2\text {Ge}_{3}}$. We find that $T_{C}$ is suppressed for low
dopings, $x \leq 0.014 $; whereas for $0.036 \leq {x} \leq 0.186 $, the samples
are antiferromagnetic with a Neel temperature, $T_{N}$, that goes through a
weak and shallow maximum ($T_N \sim$ 3.4 K for $ x \sim$ 0.07) and then
gradually decreases to 2.4 K by $x$ = 0.186. For intermediate Ni substitutions,
$0.016 \leq {x} \leq 0.027 $, two transition temperatures are inferred with
$T_N > T_C$. Whereas the $T-x$ phase diagram for
${\text{La}_{5}\text{(Co}_{1-x}\text {Ni}_{x})_2\text {Ge}_{3}}$ and the $T-p$
phase diagram determined for the parent
$\text{La}_{5}\text{Co}_{2}\text{Ge}_{3}$ under hydrostatic pressure are
grossly similar, changing from a low doping or low pressure ferromagnetic (FM)
ground state to a high doped or pressure antiferromagnetic (AFM) state,
perturbation by Ni substitution enabled us to identify an intermediate doping
regime where both FM and AFM transitions occur.
