Microbial species exhibit sophisticated interdependencies as strategies to coexist in communities. Human health and disease are critically dependent on the compositions and structures of these communities. Unraveling the underlying interdependencies would help engineer natural and synthetic microbial communities, central to modern food and healthcare applications. Here, we constructed a synthetic microbial community of seven naturally co-occurring oral bacteria and employed a bottom-up approach to understand the role of interspecies interactions in deciding the structure of this community. In particular, we focused on the abundance of the species Actinomyces viscosus, implicated in the virulence of oral microbial biofilms and dental caries. The community showed strong evidence of fifth-order interactions. The abundance of A. viscosus was high in monoculture, low in the presence of some but not all of the other species, and high again in the seven-species community. To understand these interactions, we investigated the influence of the various species in different combinations on A. viscosus. Two species, Streptococcus mitis and Lactobacillus casei, individually strongly suppressed A. viscosus. This suppression could not be reversed by any of the other species in all possible combinations, except when they were all simultaneously present. Thus, the need for the simultaneous presence of the remaining four species to overcome the influence of S. mitis and L. casei on A. viscosus implied that the seven species community structure was due to a fifth-order interaction that eclipsed the pairwise interactions. We employed a generalized Lotka-Volterra model to quantify these interactions. The interactions captured the structure of a new community containing the seven species and an additional species, validating the model and presenting the high-order interaction as a handle to tune the community structure. Overall, our study demonstrates the existence of high-order interactions that could define the structure of multispecies microbial communities.