R, (削除) 56 (削除ここまで) 54 bytes

Edit: -2 bytes thanks to pajonk

function(n,i){while(n<-n-(i==(!T%%3)+2*!T%%5))T=T+1;T}

Try it online!

This really (still...) seems to have too many parentheses... Edit: but one pair less now (thanks: pajonk).

R, (削除) 56 (削除ここまで) (削除) 54 (削除ここまで) 52 bytes

Edit: -4 bytes thanks to pajonk

function(n,i){while(n<-n-!(!T%%3)-i+2*!T%%5)T=T+1;T}

Try it online!

(削除) This really seems to have too many parentheses... (削除ここまで)
Edit: This is really pajonk's answer, now, after removing all the useless parentheses that I left in the original...

R, 56 bytes

function(n,i){while(n<-n-((!T%%3)+2*(!T%%5)==i))T=T+1;T}

Try it online!

This really seems to have too many parentheses...

R, (削除) 56 (削除ここまで) 54 bytes

Edit: -2 bytes thanks to pajonk

function(n,i){while(n<-n-(i==(!T%%3)+2*!T%%5))T=T+1;T}

Try it online!

This really (still...) seems to have too many parentheses...Edit: but one pair less now (thanks: pajonk).