An attempt at a true ELI5 is the bodies exist in what we know as spacetime, not as separate independent concepts of space and time which we perceive from our day to day experience, so we have to know a bit about the difference. Chiefly in spacetime everything always travels the same "speed" (c, the universal speed limit) and it's just a matter of how much of that speed appears as "traveling through space" and how much appears as "traveling through time". When 2 bodies warp spacetime it causes changes in the way each body's spacetime speed is distributed causing them to accelerate towards each other.
The ELI15 version is think about vectors in our normal concept of 3D space first, if I told you a body was always moving at 100 meters per second and it was 100% in the horizontal direction you'd say there was 0 meters per second in the vertical direction. Now say something curves this geometry a little bit, the body will still be traveling at 100 meters per second but now a tiny bit of that speed may appear to manifest in the vertical direction and a tiny bit less appear to manifest in the horizontal direction. Same general story with spacetime except the math is a lot more complex leading to some nuance in how things actually change.
The ELI20 version should you want to understand how to calculate the effects yourself is probably best left to this 8 part mini series rather than me https://youtu.be/xodtfM1r9FA and the 8th episode recap actually has a challenge problem to calculate what causes a stationary satellite to fall to the sun (in an idealized example) that exactly matches your question.
It's 1:1 with the relations in the equations up until the analogy of warped Euclidean space changing the vector at which point the description is functionally very similar but relativity follows very different (but also somewhat similar in a way) mathematical mechanics to the vector changing.
The "spacetime speed vector" is more formally the four-velocity and it's true that the norm of this 3 component space 1 component time vector is strictly tied to c. At the same time the four-velocity doesn't actually mathematically behave like a euclidean vector space vector where you can just add another like vector describing the effects of the warping and call it a day. In reality you have to run it through the metric tensor first (some function for the given instance that describes the geometry of warped spacetime) to get things in a coordinate space that is usable. Once you have that you actually have to run it through the geodesic equation to see what the acceleration will be as using the mapped four-vector alone will only tell you about the current velocity components in your coordinate space not the effect of the spacetime warping on something in them. These kinds of differences are the bits I swept under the rug as "nuance in how things actually change" but the net concept of the four-vector shifting components due to the warping of spacetime as an object moves along its world line is 100% the net result.
Also I can't really take credit for the method of explanation, just some of the simplified wording. I do find this explanation not only infinitely more accurate but actually easier to understand than the damn rubber sheet analogies or even improved/3D space warping analogies as they still leave out the time portion of the spacetime gradient which actually plays a bigger role in these examples.
The ELI15 version is think about vectors in our normal concept of 3D space first, if I told you a body was always moving at 100 meters per second and it was 100% in the horizontal direction you'd say there was 0 meters per second in the vertical direction. Now say something curves this geometry a little bit, the body will still be traveling at 100 meters per second but now a tiny bit of that speed may appear to manifest in the vertical direction and a tiny bit less appear to manifest in the horizontal direction. Same general story with spacetime except the math is a lot more complex leading to some nuance in how things actually change.
The ELI20 version should you want to understand how to calculate the effects yourself is probably best left to this 8 part mini series rather than me https://youtu.be/xodtfM1r9FA and the 8th episode recap actually has a challenge problem to calculate what causes a stationary satellite to fall to the sun (in an idealized example) that exactly matches your question.