After attempting many upgrades of various WP and ACF versions, I have concluded that WP 3.8 to 4.2 with ACF 4 data can not be upgraded to WP 4.3+ withACF 5.
Reason
WP 4.3 introduced a feature called split_shared_term, which affects the data used by ACF 5. ACF 4 stores the data in a manner that is re-indexed by the WP 4.3+ term splitting once it is upgraded to ACF 5. Resulting in ACF being unable to find the assigned indexes of those split terms.
I believe this is an issue with the ACF 5 database upgrade, not fully accounting for the split terms that WP 4.3+ will create from the ACF 4 data.
I have reached out to the ACF support team regarding the issue, with a general response on how the upgrade to ACF 5 may not have completed fully or an error occurred. As per their suggestion by changing the ACF version in the wp_options table and forcibly running the database upgrade again, results in duplicate data, but still invalid index references.
I managed to find a plugin that seems to mitigate the issue in ACF 4 when upgrading from WP 4.0 to 4.3, but does not work for ACF 5. The plugin is called acf-split-terms on github.
For more details about the split terms, please see https://make.wordpress.org/core/2015/02/16/taxonomy-term-splitting-in-4-2-a-developer-guide/