Here are the best pictures I have made. The C code uses fourth order Runge-Kutta with variable Δt. See Weisstein's note on Runge-Kutta for what you need to know to write the code. (See at least the pictures in this for clues as to why it works..) Here are comments on the accuracy of the method. About one million steps were used. The Java code that plots the pictures on the screen reads files, one per image. This was computed with the Pentium's 64 significant bits. I use the Mac utility "grab" to capture the screen image in a .tiff file and then Adobe's Photoshop lite to crop and label the pictures with timestamps. Photoshop then produces the .png files that your browser reads.

Each picture is for 8 time units. White dots on the curve are where the time has an integral value. I have labeled some to avoid ambiguities. Labels for times 35 thru 40 are confusing. At t = 37 and t = 38 the 5 mass (yellow) lands on the track of the 3 mass (turquois). At t = 47 the 5 mass is just back to where it was at about t = 40.6. The greatest numerical distress occurs about 15.7 which event is notable in the picture. The 3 mass is off screen between t = 49 and t = 57 after which it makes its last encounter with the other two which have already begun their final perpetual pas de deux. It passes between the other two in such a phase so as to extract enough of their potential energy to be ejected from the system.

Legend:
masscolor
3turqouis
4magenta
5yellow
0<=t<8 at t = 1.8793
ke = 2057
Δt = 6*10-8

at t = 3.8
ke = 324
Δt = 2.5*10-7

at t = 6.898
ke = 140
Δt = 10-6

8<=t<16 at t = 8.76
ke = 2344
Δt = 1.6*10-8

at t = 15.82992
ke = 48319 (Wow!)
Δt = 2.4*10-10
Δx = .0004

16<=t<24 at t = 22.965
ke = 1136
Δt = 2.5*10-7
24<=t<32 at t = 29.8015
ke = 7100
Δt = 7.8*10-9
32<=t<40 at t = 33.6715
ke = 213
Δt = 2*10-6
40<=t<48 at t = 41.209
ke = 620
Δt = 5*10-7

at t = 46.015
ke = 599
Δt = 5*10-7

at t = 47.371
ke = 1184
Δt = 1.2*10-7

48<=t<56 at t = 52.116
ke = 1509
Δt = 1.2*10-7

etc.

56<=t<62 at t = 59.777
ke = 2662
Δt = 6.2*10-8

at t = 60.6335
ke = 3067
Δt = 6.2*10-8

at t = 61.494
ke = 3126
Δt = 3.1*10-8

See the effects of some perturbations of the initial conditions