Finding the exact no. of districts in India does not seem to be trivial task (https://blog.socialcops.com/intelligence/data-stories/boundary-changes-districts-in-india/), because different agencies provide different dates depending on the latest information they have. Here, I took this issue as a data analysis task and tried finding the no. of districts in India currently and where the latest 5 districts were created. This analysis is based on two trusted datasets, one published in 2017 and another in 2018.
In this analysis, the date of creation of a district is assumed as that date mentioned in the respective Government's Gazette Notification (indicating the formation of that district).
The data file from https://data.gov.in/resources/district-wise-availability-health-centres-india-31st-march-2017, which contains information about district-wise availability of health centres in india as on 31st March, 2017, is believed to have up-to-date information about districts as on March, 2017 .
The data file from https://www.askbankifsccode.com/blog/list-of-all-states-union-territories-and-districts-in-india/ claims to have information about all districts and states as on March, 2018. The information in this file is also cross verified with the offficial data (could not find in tabular format) from the Government of India web directory http://www.goidirectory.gov.in/district_categories1.php?ou=TN.
Based on my analysis, there are 718 districts in India currently. And the latest 5 districts were created in Manipur on December 8, 2016.