I would like to update a sharepoint 2013 enterprise farm. The current build is 15.0.4971.1001 (October 2017) and the target build is 15.0.5137.1000 (May 2019). So, my question here is whether shall I directly update to the target build or update some other in-between patch (for example April 2018) before I reach the target May 2019?
Your only requirement to putting the latest patch is to have SP1 installed. As you are on Oct 2017 CU your are already there. So there is no need to install the any patch in between. But I would advise to install them more often (on monthly basis if your farm is exposed to internet) it will reduce the time required for the content DB updates and general downtime caused by upgrade.
For other secret knowledge about SP CU go to Stefan blog: https://blog.stefan-gossner.com/2019/07/09/july-2019-cu-for-sharepoint-2013-product-family-is-available-for-download/