If I want to merge metropolitan area data, from 2005 to 2016. Can I use metfips? Is this variable consistent during this period?

As stated in the METFIPS comparability tab, definitions of metropolitan areas along with their codes change over time. The codes tab provides specific documentation about when certain codes were valid for certain metropolitan areas. In particular, between 2005 and 2016, the definitions and codes changed at least once. Additionally, the metropolitan codes for 2014 onward are available here.