5 rounds, 3 on Saturday.
I decided not to play 3 games a day a long while back, since by the time the 3rd game comes along I start seeing things that are not there.
Given that.
In which round should I take a bye in order to maximize my chances maximizing my score out of 5.
I am rated 1915 & in the top of the bottom bracket(9/14) paired against an IM in round 1.
Seeing as you are already paired, it is a bit late to ask for a round one bye.
The most obvious answer is take a round three bye and get your sleep so that you are refreshed for rounds four and five.
If you don’t need a lot of sleep but may be exhausted after playing an IM then round two is plausible.
If you lose to the IM then you would be paired with a person near the top of the fourth quarter in round two, or may end up playing an even weaker player in round three after taking a round two half-point bye (definitely weaker if only zero-point byes are available).
If you draw the IM then your round two opponent would depend on how many players took a round one half-point bye. With no late entrants, the IM possibly paired up against the bottom 1-0 would be balanced by the lowest 0.5-0.5 (maybe you if yours was the only draw) paired down against the top 0-1, leaving the remaining players to be paired simlarly to round one with you still in the bottom half. With late entrants you might be paired down in round two if a majority of them are for players lower rated than you.
A half point bye in round two would make you even going into round three and slightly more likely than not to be paired up.
If you beat the IM (granted it is unlikely but even IMs are human) then you would definitely be paired up in either two or three depending on when you took the bye with a round two pairing likely more difficult than a round three pairing.
So if sleep is not an issue at all then you are asking to decide whether or not you want to play tougher or easier opponents. There is plenty of room for fluctuation but I think the odds seem to slightly favor tougher opponents with a round three bye. Things look close enough that if sleep is even a minor issue then round three looks better for a bye (the joker in the deck being whether or not you’d be temporarily drained after your round one game).
My mistake, Not paired, just looking at pr-enries
What about a round 1 bye
If you want to sleep in and be more refreshed for rounds two and three then a round one bye would be fine.
Since you are on the cusp your actual round one pairing would depending on the later entries. If you end up in the bottom half then the previous note applies for round two or three byes. If you end up in the top half then you have the following:
Win - likely to have a somewhat stronger opponent in round two before a bye than in round three after;
Draw - depending on the late entrants, the round two opponent is more likely to be similar to the round one opponent
Loss - likely to have a somewhat weaker opponent in round two before a bye than round three after
For a round one bye, the round two opponents depend on the ratings of the late entrants (essentially including you). If you are the only late entrant then you might end up playing the strongest 0.5-0.5 player in round two (easily possible if you were just over the midpoint and there is an even number of 1-0 players) or the weakest (if you were just over the midpoint and there is an odd number of 1-0 players).
With the vagaries of Swiss pairings, the overriding concern is generally going to be which timing will leave you in better shape to play the other rounds regardless of who the opponent is.
assuming you are almost certain to lose to the IM, you take your bye in the first round, and look forward to an easier pairing. 1/2 a point when you are nearly guaranteed 0 points is an alright deal.
though, the IM will help your avg rating of opponents so maybe you take your lumps, get an easier pairing in the 2nd round, and take a bye in the 3rd where you were likely to again be paired up.
I decided not to take a bye, but played the price by losing this game:
I felt fine for most of the game, but had trouble focusing right at the end 
Never will I pay 3 games on the same day!
CAISSA PALANG (1677) vs IVAN WIJETUNGE (1911)
[D13]
Laredo (3), 16.04.2011
1.d4 c6 2.c4 d5 3.cxd5 cxd5 4.Nf3 Nc6 5.Nc3 Nf6 6.Bf4 e6 7.e3 a6 8.Be2 Be7 9.0-0 Nh5 10.Bg3 0-0 11.Rc1 Bd7 12.Qd2 b5 13.Rfe1 f6 14.Red1 Na5 15.b3 [15.Bc7 Qxc7 16.Nxd5 Qd8 17.Nxe7+ Qxe7 18.Qxa5] 15…Ba3 16.Rc2 Nc6 17.Nb1 Be7 18.Rdc1 Nxg3 19.hxg3 Qb6 20.a3 Bd6 [20…Na5 21.Rc7 (21.Qd3 Be8 22.Nh4 g5) 21…Nxb3] 21.Qd3 Ne7 22.Qd2 Qb7 23.b4 Rfc8 24.Rxc8+ Nxc8 25.Ne1 Nb6 26.Nd3 Nc4 27.Qc3 Bc6 28.Nc5 Qe7 29.Nd2 a5 30.Nxc4 dxc4 [30…axb4 31.axb4 dxc4] 31.Ra1 e5 32.Bf3 Bxf3 33.gxf3 a4 [33…Qa7 34.Rd1 axb4 35.axb4 Qa3] 34.Re1 Re8 35.Rd1 exd4 36.Qxd4 Bxc5 37.bxc5 Rc8 38.Qd5+ Kf8 39.c6 Qc7 [39…Qe5 40.Qd7 Qe8 41.Qb7 Rxc6 42.Rd7 Rc8 43.Rf7+ Qxf7 44.Qxc8+ Qe8] 40.Qc5+ Kg8 41.Rd7 Qe5 42.Qxe5 fxe5 43.c7 0-1
http://www.uschess.org/msa/XtblMain.php?201104178371.1-12511643