The short answer: "baptism" here is both symbolic and instrumental, but definitely is NOT referring to water baptism.
I submit that Paul is not referring to water baptism AT ALL, but something much greater. Since "the burden of proof must be on the [one who holds the] position that Paul is not thinking of water baptism", let me suggest five lines of reasoning to prove the Reformed position:
1. His words indicate baptism with something other than water, namely, death:
Therefore we were buried with Him through baptism into death.
This is akin to the statements elsewhere in the New Testament which are clearly not referring to water immersion, e.g. John the Baptist's attestation regarding Jesus' baptism:
I indeed baptize you with water unto repentance, but He ... will baptize you with the Holy Spirit and with fire. [Matthew 3:11]
Paul uses this non-water sense of baptism in at least two places:
Moreover, brethren, I do not want you to be unaware that all our fathers were under the cloud, all passed through the sea, all were baptized into Moses in the cloud and in the sea [1Cor 10:1,2]
For by one Spirit we were all baptized into one body—whether Jews or Greeks, whether slaves or free—and have all been made to drink into one Spirit. [1Cor 12:13]
This latter verse could be construed as "baptised with water into one body". But the Spirit doesn't use water for Baptism, He baptizes us with Himself; priests and ministers use water. That is not what Paul meant.
2. The whole tenor of his argument suggests something greater than water baptism.
The phrase in v.5, "baptism into death", is more reminiscent of his expression, "crucified with Christ"; crucifixion is certainly not symbolized by water baptism. But what Paul is referring to here is, in the next verse , the same as crucifixion:
knowing this, that our old man was crucified with Him.
The real teaching of this passage is the believer's union with Christ, which, yes, is symbolized by baptism. But when Paul says "baptism" in this context, he is referring to that greater, mystical union that takes place quite apart from any work performed by the believer, including water baptism1. In the phrase "united together in baptism" [v.5] the sense is being planted together, or grafted into Christ. That is the sense of σύμφυτος (sumphutos).
3. Paul never taught ceremonial works as effectual, either of justification or regeneration.
For one thing, this would contradict his express theme, "not of works". It would also contradict his pervasive emphasis on the blood of Jesus as the atonement for sin and the propitiation of God's wrath.
Many see the word "baptism" in this passage and interpret it as a teaching on water baptism, even going so far as to give water baptism the central role in regeneration. This is exactly the sacramentalist interpretation, viz., that God's grace is actually communicated VIA the water (or wafer or wine) to the believer. To the First Century believers, baptism was ONLY a sign of the new birth that had already begun in the believer. So baptism was never given to unbelievers. To suggest that water baptism begins or even aids the new birth is, in the words of the old saw, "putting the cart before the horse." The believer is already alive in Christ when he comes forward to be baptized. It cannot, then, be instrumental in Pauline theology.
4. Baptism, as a mere symbol, cannot make us united with Christ.
Rejecting his use of baptism as effectual isn't the whole conclusion. If he is referring to water baptism as a symbol, to suggest that a mere symbol is the thing that joins us to Christ, makes us one with all Christians, makes us new creations, raises us from the dead, washes away our sins and "seats us together with Christ in the heavenly realms" [Eph 2:6], is to suggest that the symbol is greater than the grace and work and blood of the Lord Jesus. This is not Pauline, and not logical.
5. To argue for water baptism in this passage goes directly against Paul's own view of the importance of baptism:
Besides, I do not know whether I baptized any other.
It wasn't an event he recorded or even made a mental note of, "Because", he says,
Christ did not send me to baptize, but to preach the gospel. [1Cor 1:16,17]
1 Unless you reject Paul's pervasive doctrine of sola fide, in which case there isn't much ground in discussing any of his teachings, on baptism or anything else.