I'd actually advise you to upgrade JIRA to the latest version which has this feature: https://confluence.atlassian.com/display/JIRA062/Auditing+in+JIRA
There is a (paid) third-party plugin that you can use for this on JIRA 5.1: https://marketplace.atlassian.com/plugins/com.plugenta.jiraauditor
I hope this helps! :)
Audit logs are not available on JIRA 5.1. This feature has been partially implemented on JIRA 6.2 and you can find more information about it on the document below:
You may refer to our central feature request for more details about this feature and some possible alternatives (plugins) which you may use on JIRA 5.1:
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