The IPIP scales are in the public domain: https://ipip.ori.org/
They are intended to have no restrictions on use (see https://ipip.ori.org/newPermission.htm ).
See in particular, the section on multi-construct inventories. I think the most popular Big Five measures would be
- Big Five Aspects Scale: It has 100 items and measures the Big Five as well as 2 aspects per Big Five. It's a nice compromise between just measuring the Big Five and the much longer facet-level measures (e.g., NEO PI R, IPIP NEO 300, etc.)
- Goldberg's IPIP 50.
- IPIP NEO 50
- IPIP NEO 300. This is modelled on the NEO PI R. So it measures 30 facets as well as the Big Five that are designed to be similar to the NEO PI R.
A major difference between Goldberg's IPIP 50 and IPIP NEO 50 is the openness factor. For Goldberg it is intellectance (i.e., intellectual engagement and self-rated intellect), whereas IPIP NEO 50 is openness to experience (i.e., some intellectual engagement, but also creative interests, unconventionality, etc.).
LEFFI: The Less Evaluative Five Factor Inventory is a new measure that is explicitly in the Public Domain (disclosure: it was developed by Joshua Wood and me). It is designed to have lower levels of item-level social desirability than some measures of the Big Five.