The very wide binary asteroid (VWBA) population is a small subset of the population of known binary and multiple asteroids made of systems with very widely orbiting satellites and long orbital periods, on the order of tens to hundreds of days. The origin of these systems is debatable, and most members of this population are poorly characterized. Aims. We aim to develop orbital solutions for some members of the VWBA population, allowing us to constrain possible formation pathways for this unusual population. Methods. We compiled all available high-angular-resolution imaging archival data of VWBA systems from large ground- and space-based telescopes. We measured the astrometric positions of the satellite relative to the primary at each epoch and analyzed the dynamics of the satellites using the Genoid genetic algorithm. Additionally, we used a NEATM thermal model to estimate the diameters of two systems, and we modeled the orbit of Litva's inner satellite using photometric light curve observations. Results. We determine the effective diameters of binary systems (17246) Christophedumas and (22899) Alconrad to be 4.7 +/- 0.4 km and 5.2 +/- 0.3 km, respectively. We determine new orbital solutions for five systems, (379) Huenna, (2577) Litva, (3548) Eurybates, (4674) Pauling, and (22899) Alconrad. We find a significantly eccentric (e = 0.30) best-fit orbital solution for the outer satellite of (2577) Litva, moderately eccentric (e = 0.13) solutions for (22899) Alconrad, and a nearly circular solution for (4674) Pauling (e = 0.04). We also confirm previously reported orbital solutions for (379) Huenna and (3548) Eurybates. Conclusions. It is unlikely that BYORP expansion could be solely responsible for the formation of VWBAs, as only (4674) Pauling matches the necessary requirements for active BYORP expansion. It is possible that the satellites of these systems were formed through YORP spin-up and then later scattered onto very wide orbits. Additionally, we find that some members of the population are unlikely to have formed satellites through YORP spin-up, and a collisional formation history is favored. In particular, this applies to VWBAs within large dynamical families, such as (22899) Alconrad and (2577) Litva, or large VWBA systems such as (379) Huenna and NASA's Lucy mission target (3548) Eurybates.