Problems with Fourier

hello everyone
I need help with this
when I introduce this commands I didn't get the right answer, and I don't know why, somebody can help me.
For example

clear all
r = 'sin(5*t)';
syms t w;
f = eval(r)
fourier(f)
F = fourier(f);
ifourier(F,'t')

and the result is:

f =

sin(5*t)

%fourier transform which is wrong
ans =

-pi*i*(dirac(w - 5) - dirac(w + 5))

%and the inverse fourier transform which is wrong too
ans =

i/(2*exp(5*i*t)) - (i*exp(5*i*t))/2

where is the problem???, Why is wrong???
 

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