Manipulate -> Pause Play at specific conditions

Manipulate by default uses Manipulator which doesn't seem to support dynamic values for the AnimationRunning option. However you could use ControlType -> Animator.

Here's a possible approach where by adding two extra control variables I can stop the animation after i reaches 5 on the first run.

Manipulate[
  If[initialRun && i >= 5, running = False; initialRun = False];
  Plot[i*Sin[x], {x, 0, 10}, PlotRange -> 10]
  ,
  {initialRun, {True, False}, ControlType -> None},
  {running, {True, False}, ControlType -> None},
  {i, 1, 10, ControlType -> Animator, AnimationRate -> 3, 
     RefreshRate -> 60, AnimationRunning -> Dynamic[running]}
]

Note that if the user interacts with the animator before it gets paused by the Manipulate, the pausing will still happen whenever the value of i is 5 or greater first.

For a version with more than one breakpoint, replace the initialRun boolean with an integer counting how many runs have happened:

With[{breakPoints = {2, 4, 8}},
  Manipulate[
    If[runNumber <= Length[breakPoints] && i >= breakPoints[[runNumber]],
      running = False; runNumber++
    ];
    Plot[i*Sin[x], {x, 0, 10}, PlotRange -> 10]
    ,
    {runNumber, 1, ControlType -> None},
    {running, {True, False}, ControlType -> None},
    {i, 1, 10, ControlType -> Animator, AnimationRate -> 3, RefreshRate -> 60, AnimationRunning -> Dynamic[running]}
  ]
]

The credit goes to @Gerli, who arrived first. Difference is that mine uses DynamicModule

DynamicModule[
 {s = True},
 Manipulate[
  If[i > 5, s = False, s = True];
  Plot[i*Sin[x], {x, 0, 10}, PlotRange -> 10],
  {
   i, 1, 10
   , ControlType -> Animator
   , AnimationRunning -> Dynamic[s]
   }]
 ]