Just browsed through the app. It gets John 5 correct, unlike the ESV. It translates it "of himself" rather than "authority."
I know this is a common criticism of the ESV, many claiming the ESV advocates for ESS here (as well as in similar places like John 8:28 and 14:10), but I just don't see it. For one thing, the translation of ἀπ’ ἐμαυτοῦ as "of my own authority/initiative" is not unique to the ESV. The RSV (which means the ESV actually didn't originate this rendering for themselves, but rather retained it ), NASB95, NET, NKJV, Amplified, and ISV all translate it this way.
Second, translating the verse this way does not necessitate an ESS understanding of Jesus' words. It seems to be to be a broad consensus from the Reformed "heavy hitters" that the words Jesus is using here does not refer to himself as God, but as the Messiah in the flesh:
"Our Saviour’s meaning is plainly this: The Son neither willeth nor can do any thing, but what the Father willeth and doth in him; therefore he is one in essence with the Father, and equal to him. For what things soever he doequoth, these also doeth the Son likewise: the Son doth those things which the Father doth; and, as the Messias, he doth those things which the Father willeth to be done."
—Matthew Poole, Annotations Upon the Holy Bible, 3 vols. (New York, NY: Robert Carter and Brothers, 1853), 3:303.
"[H]e did nothing of himself, not of himself as man, of himself alone, of himself without the Father, with whom he was one."
—Matthew Henry, Matthew Henry’s Commentary on the Whole Bible: Complete and Unabridged in One Volume (Peabody, MA: Hendrickson Publishers, 1994), 1968).
"The discourse does not relate to the simple Divinity of Christ, and those statements which we shall immediately see do not simply and of themselves relate to the eternal Word of God, but apply only to the Son of God, so far as he is manifested in the flesh."
—John Calvin, Commentaries, John 5:19.
"[Jesus speaking:] 'The doctrines which I preach among you are a proof of what I assert, and to them I appeal; for these are not of myself, as man, but the father that dwelleth in me.'"
—John Gill, Commentaries, John 14:10.
I say all this as someone who doesn't really care for the ESV, and as someone who opposes ESS. I've just seen this accusation leveled against it, and I just don't think it holds weight. If anything, we could fault the ESV Study Bible for being unclear in its note on John 5:19. But, even then, I see nothing there that 1) teaches ESS explicitly or 2) teaches anything different than the men I quoted above say.