I'm rusty at this, but I want to say it would have 4 peaks...
-The C1 with 3H would give 1 peak (singlet) 2nd furthest peak.
-The C3 with 2H would give Another one (Triplet) furthest peak.
-The C4 with 2H would give another peak (Multiplet) 3rd furthest peak.
-The C5 with 3H would give the 4th peak (Triplet) 4th furthest peak.
Ok take a look at the picture above, the C's I will refer to are 1,2,3,4,5 respectively.
The Singlet (1 Strong Peak) from Carbon 1 would result because it has 3 Hydrogens that are in the 'same environment' per say. Each is 1 bond away from C2 which doesn't have any Hydrogens attached, this is why it is a singlet (it is further DOWNFIELD on the HNMR plot because it is close to an electronegative O atom).
C3 would result in a Triplet (1 taller peak surrounded by 2 shorter peaks) because its Hydrogen atoms are next to C4 which has 2 H's which are in a "different environment" than the ones on C3. (Sorry this is hard to explain without having you here to actually see what I'm talking about).
C4 would result in a Multiplet because it's H's are surrounded by C3 and C5 which each have 2 and 3 Hydrogens (respectively) that are in different 'environments' than C4's.
*By different environment, I mean that the Hydrogens on the carbons do not have the same connectivity as the hydrogens of the adjacenet carbons. Remember, when looking at HNMR data, you only consider the Hydrogens that are adjacent to the atom you are examining.
Like I said before, it's tough for me to explain without having you here next to me to show you what I'm talking about.