Parametric dependence of the intensity of 182 Å Balmer-𝛼 line $(C^{5+}; n = 3 \rightarrow 2)$, relevant to xuv soft X-ray lasing schemes, from laser-produced carbon plasma is studied in circular spot focusing geometry using a flat field grating spectrograph. The maximum spectral intensity for this line in space integrated mode occurred at a laser intensity of $1.2 \times 10^{13}$ W cm^-2. At this laser intensity, the space resolved measurements show that the spectral intensity of this line peaks at $\sim 1.5$ mm from the target surface indicating the maximum population of C⁵⁺ ions $(n = 3)$, at this distance. From a comparison of spatial intensity variation of this line with that of C⁵⁺ Ly-𝛼 $(n = 2 \rightarrow 1)$ line, it is inferred that $n = 3$ state of C⁵⁺ ions is predominantly populated through three-body recombination pumping of C$^{6+}$ ions of the expanding plasma consistent with quantitative estimates on recombination rates of different processes.