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I assumed that the preview would use the shadow files so the large raw file size would not be an issue.
Again, the performance has nothing to do with raw file size and everything to do with how the video is encoded. It takes a finite amount of time to decode the changes from frame to frame in an H.265-encoded video, and PD has to do that for all 15 frames that will eventually be discarded to create the correct content for the 16th frame. Your computer simply can't do that in real time during the timeline preview.
Pre-producing the sped up clip is the simplest way around the issue, or you can convert the clip into an intermediate codec, like MagicYUV. You will then be able to preview in full quality without any lag even though the raw file size is many times larger than the original clip. That's because each frame is stored as a full image instead of a list of changes from the previous frame so it's effortless for PD to skip 15 frames.
There's a free and also a low cost version of MagicYUV available
here, and the quickest way to make this work is to convert the clip then save it to the same folder as your original c115.MP4 clip..
With PD closed, rename the extension of the original clip to something like
.old, then change the name of the MagicYUV clip to c115.MP4. When you open PD again, it wiall automatically use the new clip in your existing project and you'll see perfect performance right away, assuming you haven't made any other significant edits, like color corrections or CLUTs.
If you have made those kinds of edits, pre-producing is really the best option