A systematic study of the magnetic properties and the Hall effect was performed on pulsed laser deposited 5% cobalt doped $(\mathrm{La},\mathrm{Sr})\mathrm{Ti}{\mathrm{O}}_3$ thin films, especially grown at high substrate temperature. The system is found to be superparamagnetic in nature as evidenced by several protocols of magnetic measurements. Nevertheless, the anomalous Hall effect (AHE) is observed in the system, the profile of the measured Hall resistivity vs magnetic field being found to be identical to the magnetic hysteresis loops. This highlights the limitations of AHE as a tool to test the intrinsic nature of ferromagnetism in a diluted magnetic system, supporting our previous report for the $\mathrm{Co}:\mathrm{Ti}{\mathrm{O}}_2$ case [S. R. Shinde et al., Phys. Rev. Lett. 92, 166601 (2004)]. It is believed that the magnetic clusters polarize nearby electrons and the nonzero polarization leads to a net transverse current because of the spin dependent scattering, which gives rise to the observed AHE. We found that the magnitude of the AHE signal observed in the current extrinsic diluted magnetic semiconductor (DMS) is much lower (by a few orders of magnitude) than that found in the intrinsic long range ferromagnetic ordered DMS, which raises the possibility for using this magnitude, rather than the occurrence of AHE, as a criterion for intrinsic or extrinsic diluted magnetic system.