We built a grid of photoionization models and compiled already available observational emission line intensities ($rm 1000 : < : lambda(AA) : < : 2000$) of confirmed star formation regions and Active Galactic Nucleus (AGNs) in order to classify five Ly$alpha$ emitter (LAE) objects at high redshift $(5.7 : < : z : < :7.2)$. We selected objects for which at least one metal emission-line was measured. The resulting sample is composed by the objects RXCJ2248.7-4431-ID3, HSCJ233408+004403, COSY, A1703-zd6, and CR7 (clump C). The photoionization models were built assuming a Power Law (associated with the presence of an AGN), a Direct Collapse Black Hole (DCBH), and Population II stars for the ionizing source. The resulting models were then compared with observational emission-line ratios in six diagnostic diagrams to produce a spectral classification of the sample. We found that CR7 (clump C), HSCJ233408+004403 and COSY probably have a non thermal ionizing source (AGN or DCBH) while the RXC J2248.7-4431-ID3 and A1703-zd6 seem to host a stellar cluster. Detailed photoionization models were constructed to reproduce observational emission line ratios of the sample of LAEs, and to derive chemical abundances and number of ionizing photons $Q(rm H)$ of these objects. From these models, we found metallicities in the range $(Z/Z_{odot})=0.1-0.5$ and $log Q(rm H) : > : 53$. Values for C/O abundance ratio derived for the LAEs seem to be consistent with those derived for local star forming objects with similar metallicities, while an overabundance of N/O was found for most of the LAEs.
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