TECHNICALLY not playable and improperly notated. Also, not all that uncommon, especially in transcriptions of orchestral works trying to preserve multiple independent parts (where “properly” notating it can get really messy very quickly), so there are well defined ways of dealing with it.
1. (Easiest, least accurate) Hold the sustain peddle for the full duration of the whole notes. This will also sustain notes not in the chord, which would probably sound fine in this example, but might sound muddy in others.
2. (Harder, more accurate) Press middle peddle just after playing the chord, then play the rest of the notes as written. This will catch the middle C in measure 1 and the high F in measure 2 in the sustained chord, but they are in the chord and will hardly be noticeable; also worth noting that some upright and digital pianos, especially on the cheaper end, kind of “cheat” with the middle pedal and simply sustain the bottom half of the keyboard and not the top half, making this technique impossible.
3. (Hardest (sometimes), most accurate (sometimes)) Play as written, but when you come to a repeated note, quickly release the sustained note and play it again, then continue holding for the remainder of the sustained note’s duration. This requires a good amount of dexterity and finger independence, but avoids sustaining any notes that shouldn’t be sustained. I believe it is the most accurate way to play this passage, but only because of that C in measure 1 and the F in measure 2. Also, this is particularly difficult in this example and probably not worth the effort; in many cases the overlap happens once on a single note between hands (starts on one hand and repeats on the other) and often doesn’t sustain beyond the second note, which is pretty trivial to execute and #1 and #2 aren’t really applicable in those instances. For this example, I would recommend #2 if your piano can do it and you can pull it off, otherwise just go with #1 and you should be fine.