There are extremely large differences in the way that ACF4 and ACF5 stored information. There is an upgrade guide for this https://www.advancedcustomfields.com/resources/upgrade-guide-version-5/
In addition to this, depending on what version of WP you started with there have been changes in the way WP stores data, as one example in 4.2 there was a split of taxonomy terms when associated with more than one post type and these changes also effected the way ACF stored data.
There are also function in ACF that were available and other things that had name changes that could cause a crash to happen.
Another thing that can cause errors is the PHP version on your server. Many things in both WP and ACF will not run correctly if the server is running an older version of WP and the reverse is true, some things will crash if you’re running the latest PHP and a plugin has not been updated to work on that PHP version.
More than likely, on a site this old I would have updated WP to the most recent minor version, for example if they were on WP 4.4.3 I would have updated to 4.4.21 and then left it there. But this really depends on where you started. As Daniel said, sometimes it’s just better to leave things alone. After a certain amount of time a site needs to be rebuilt, that’s just the way it is.
Beyond this what is needed is a better explanation of why the site is crashing and I would recommend turning on error display so that you have the information you need to debug the issues https://codex.wordpress.org/WP_DEBUG
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