Short answer
No. Qur'an 5:116 does not describe the Trinity at all. It records a question God (﷾) will ask Jesus on the Day of Judgement: did he tell people to worship him and his mother as gods? That question is about what people did, not about what a church council decided. And some people did worship Mary. Epiphanius, a fourth-century bishop, wrote against Christians in the Roman province of Arabia who offered cakes to her, and he condemned them for it. When the Qur'an speaks of the Trinity itself, in other verses, it never counts Mary as one of the three. It simply says "Say not Trinity", because God (﷾) is one. Islam's answer is plain: God (﷾) is one, and neither Jesus nor his mother is divine.
Full explanation
What 5:116 actually says
The verse is set on the Day of Judgement. God (﷾) asks Jesus whether he told people to take him and his mother as gods beside God (﷾). Jesus denies it. In the next verse he says he only ever told them to worship Allah (﷾), his Lord and theirs. So the verse is a question about worship given to Jesus and Mary. It does not state any creed (a statement of what a church believes).
“And behold! Allah will say: "O Jesus the son of Mary! Didst thou say unto men, worship me and my mother as gods in derogation of Allah'?" He will say: "Glory to Thee! never could I say what I had no right (to say). Had I said such a thing, thou wouldst indeed have known it. Thou knowest what is in my heart, Thou I know not what is in Thine. For Thou knowest in full all that is hidden.”
“"Never said I to them aught except what Thou didst command me to say, to wit, 'worship Allah, my Lord and your Lord'; and I was a witness over them whilst I dwelt amongst them; when Thou didst take me up Thou wast the Watcher over them, and Thou art a witness to all things.”
Where the Qur'an speaks of the Trinity
The Qur'an speaks about the Trinity in other verses. It rejects saying God (﷾) is "one of three" and tells Christians "Say not Trinity". Neither verse counts Mary as one of the three. Two verses after 5:73, the Qur'an gives a plain reason why neither Jesus nor his mother is divine: both had to eat food. So the Qur'an denies that Mary is divine, just as it denies it of Jesus. But nowhere does it place her among the three.
“O People of the Book! Commit no excesses in your religion: Nor say of Allah aught but the truth. Christ Jesus the son of Mary was (no more than) a messenger of Allah, and His Word, which He bestowed on Mary, and a spirit proceeding from Him: so believe in Allah and His messengers. Say not "Trinity": desist: it will be better for you: for Allah is one Allah: Glory be to Him: (far exalted is He) above having a son. To Him belong all things in the heavens and on earth. And enough is Allah as a Disposer of affairs.”
“They do blaspheme who say: Allah is one of three in a Trinity: for there is no god except One Allah. If they desist not from their word (of blasphemy), verily a grievous penalty will befall the blasphemers among them.”
“Christ the son of Mary was no more than a messenger; many were the messengers that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how Allah doth make His signs clear to them; yet see in what ways they are deluded away from the truth!”
Christians who did worship Mary
Epiphanius of Salamis was a Christian bishop who wrote around 375. He describes the Collyridians, women in the Roman province of Arabia who offered cakes in Mary's name. He condemned this as giving Mary the worship that belongs to God (﷾). So the worship of Mary that 5:116 asks about was real among Christians in the Roman province of Arabia. A Christian bishop condemned it himself.
Epiphanius, a fourth-century bishop, describes women in the Roman province of Arabia, whose practice came from Thrace, who on a set day offered a small loaf or cake (kollyris) in the name of Mary, and so were called Collyridians. He condemns it: Mary is to be honoured, but she is not to be worshipped, for worship belongs to God alone.
Verse by verse
Qur'an 5:116 — Surat al-Ma'ida (The Table), verse 116
“And behold! Allah will say: "O Jesus the son of Mary! Didst thou say unto men, worship me and my mother as gods in derogation of Allah'?" He will say: "Glory to Thee! never could I say what I had no right (to say). Had I said such a thing, thou wouldst indeed have known it. Thou knowest what is in my heart, Thou I know not what is in Thine. For Thou knowest in full all that is hidden.”
Cited for
The Qur'an thinks the Christian Trinity is God, Jesus and Mary.
The response
The verse never speaks of 'three'. It asks whether Jesus told people to worship him and his mother. Some people did worship Mary, and Epiphanius condemned them for it. Two other verses do speak of 'three' (4:171 and 5:73). Yusuf Ali translates their 'three' as 'Trinity'. Neither verse counts Mary as one of the three.
Where it lands — The verse is about worship people really gave to Mary, not a mistaken definition of the Trinity.
Perspectives
The critic's objection
The Qur'an gets the Trinity wrong. It thinks Christians worship Father, Son and Mary, which no church has taught.
Qur'an 5:116 speaks of Jesus and his mother being taken as gods. Critics read this as the Qur'an's picture of the Trinity.
Rebuttal
No church creed puts Mary among the three, and the Qur'an never says one does. Verse 5:116 asks about worship given to Jesus and Mary, and some Christians did worship her. Verse 5:75, two after 5:73, names Jesus and his mother to show neither is divine: he was only a messenger, and both ate food.
The Islamic perspective
Qur'an 5:116 is a question about worship, and the worship of Mary was a real practice that a Christian bishop condemned. The Qur'an rejects the Trinity separately and never counts Mary as one of the three.
In 5:116 God (﷾) asks Jesus whether he told people to worship him and his mother as gods. The verse defines no creed.
The verses that reject the Trinity, 4:171 and 5:73, never count Mary as one of the three.
Epiphanius was a fourth-century bishop. He condemned Christians in the Roman province of Arabia who offered cakes to Mary as an act of worship.
The Qur'an teaches that neither Jesus nor Mary is divine, since both needed food.