As per section 139(2) and 139(4) of the Companies Act,2013 all listed companies and certain categories of unlisted public companies and private companies to mandatorily rotate their auditors (whether such auditor is an individual or a firm) once their auditor has served office as an auditor for a period of 1 term of 5 years for an Individual (read Proprietorship firm) or 2 terms of 5 years for Audit firm (read Partnership firm).
Do note that the status of category of the firm shall be seen at the time of 1st AGM which will be held after the completion of 3 years from 01.04.2014 i.e. probation period given in the act as mentioned in the Companies (Removal of difficulties) third order, 2016.
So as per above provisions whether you are a proprietary or a partnership firm will be seen in your 1st appointment when section139(2) was applicable on you i.e. 1st agm for 2017.
If you are a proprietary firm then, then even if you are converted into a partnership firm later on the maximum tenure you can be appointed shall be 1 term of 5 years.
If at time of 1st agm you already have been converted into a partnership firm, then you can be appointed for 2 terms of 5 years.