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If I were to under the effects of a jump spell would it be possible to jump over a medium-sized enemy and avoid an opportunity attack? Assume my speed is 60' and my strength modifier is +5.

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Yes

The Jump spell triples your distance when you are using it to jump. There are two options for jumping described in the PHB: Long Jump and High Jump both on page 182 of the PHB.

High Jump seems like it would be applicable here, but really Long Jump is. Your stated goal is to jump over someone without provoking an attack of opportunity, thus you're looking to clear at least 15' laterally (5' for the target you're jumping over as well as all squares they threaten) without touching the ground and you want to clear enough height to jump over someone. Based on the criteria of your related question, I'm going to assume a 5'8" medium orc, so you need to jump over 10'8" (height of the creature plus 5' for threatened area).

So let's break this into parts:

  1. Long jump first (i.e. is this even possible): With a +5 to Strength, or a Strength of 20, this is absolutely possible. As stated in the Long Jump rules, your jump distance is equal to your Strength score, or 20 feet in this case. Since the Jump spell has tripled this, it's now 60 feet, so this it is certainly viable to meet the 15' of horizontal distance.
  2. The long jump rules assume the height of your jump is irrelevant and suggest a DC10 Athletics check if you need to clear a low obstacle, specifically one that's no taller than 1/4 of your jump's distance). Under the stated conditions, you are able to jump 60' horizontal, so for you, a low obstacle would be one that's 15' high. As a result, you absolutely meet the vertical requirement plus a little room for error if you make a DC10 Athletics check.
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    \$\begingroup\$ Opportunity attacks are defined within the creatures reach of the space it commands. Height isn't a factor - the clearance distance should be 10'. \$\endgroup\$ – NautArch Nov 29 '17 at 1:21
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    \$\begingroup\$ @NautArch does that not assume a grid system? iirc the baseline rules do not include a grid system. Even without a grid, how does one define the bounds of vertical reach? does such a thing exist? \$\endgroup\$ – Premier Bromanov Nov 29 '17 at 4:28
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    \$\begingroup\$ Reach of a character without a reach weapon is 5', not 10'. Being outside of 5' puts you out of reach unless they have a polearm or the like. Grid system or not. That means you need to get to a height equal to or greater than their height + 5'. \$\endgroup\$ – J. A. Streich Nov 29 '17 at 5:37

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