Colleges in Delhi

B.Des eligibility criteria of NIFT is given below.
1. Qualifying Age: Maximum age should be 23 years as on 1st October, 2019. The upper age limit may be relaxed by a period of 5 (five) years for candidates of Scheduled Caste/Scheduled Tribe/ Person with Disability (PWD) categories.
2. Educational qualification for Bachelor of Design (B.Des) Programmes (Fashion Design / Leather Design / Accessory Design / Textile Design / Knitwear Design / Fashion Communication) : The +2 level examination in the 10+2 pattern of examination of any recognized Central/State Board of Secondary Examination, such as Central Board of Secondary Education / State Board New Delhi, and Council for Indian School of Certificate Examination, New Delhi.
So from above age criteria is very important. The Gap of 5 years after 12th is not a big issue because you have completed your graduation during this period. So you can be eligible if meeting the age criteria as above.
Further you are also eligible for M.Des course of NIFT because there is no age restriction for M.Des course. While the eligibility criteria is Graduation in any discipline. The admission in M.Des are also done through NIFT entrance exam.

M.Sc Hospitality Administration (Maharashtra) is a regular mode programme in collaboration with the National Council for Hotel Management and Catering Technology, (NCHMCT) NOIDA. The admission in the asked course is done by NCHMCT through and entrance exam M.Sc. HA. Eligibility Criteria B.Sc. Degree in Hospitality and Hotel Administration from NCHMCT-IGNOU; or Bachelor's Degree in Hotel Management from a recognized University and the Institute is approved by AICTE. Candidates appearing in the final semester/final year exam (but passed all the papers in all earlier semesters/years) of the above said Degrees and able to submit their complete Bachelors's Degree can also apply. So from above, you have to apply through NCHMCT website http://nchm.nic.in/.