Given an equation in the form
#color(white)("XXXX")##y = # an expression solely involving #x#
and
#color(white)("XXXX")#a value for #x#;
simply replace the #x#'s in the expression with the value given for #x# and evaluate using normal rules (which may involve the use of a calculator).
The fact that the expression involves a trigonometric function does not effect this general principle.
Demonstrating with the given equation #y=4sin(2(x+1)) +2#
and #x=5#
#color(white)("XXXX")#(by the way, I've assumed your sin function is using a radian and not a degree argument)
#y = 4sin(2(5+1))+2#
#y= 4sin(12)+2#
#color(white)("XXXX")#using a calculator to look-up #sin(12)#
#y= 4(-053657)+2#
#y= -0.14629#
#color(white)("XXXX")#...and, yes, I did continue to use a calculator for this.
