Article 5 is the German version of "freedom of speech". It specifically protects the people from the state (i.e., from the legislature, executive and judiciary). Nothing more and nothing less.
Article 5 makes sure that the state does not create laws or executive policies that go against the freedom of speech. It directly limits the power of the state, and thus indirectly increases the power of individuals and organizations. Amongst others, it forbids introducing general state censorship.
Paragraph 3 specifically protects arts, science and education from the state.
Art 5 is not absolute; if there are conflicts with other articles, a resolution has to be found so the conflicting laws can be made concordant. This is a common principle of the German constitution. Examples very relevant to freedom of science: protection of personal data, animal welfare, etc. - so the state can and does most definitely place limits on what/how science can be done in these circumstances.
Regarding your question: Art 5 only talks about the relationship between the state and individuals/organizations. It says nothing about how individuals or organizations interact with each other. It does not tell us whether an organization can forbid a person from and how to communicate. These things happen all the time; i.e. a non-state organization can easily negotiate an NDA with you to forbid you from talking about specific topics. You can not go and publicly tell untrue allegations against someone (well you can, but they then have recourse against you). You can not publish state secrets. And so on and forth.
But most specifically, Art 5 does not have influence about how you interact with your uni. At the end of the day you will have a contract with them, and whatever is in the contract "counts". If your contract says that you are paid for working on some specific scientific topic, that's what you have to do. If the contract says that someone at the uni is "weisungsbefugt" (i.e., your direct "boss"), then you have to do what they say, within reason and within the purview. If your contract links your continued employment at the uni to certain performance indicators (maybe related to communication - e.g. publishing about certain topics), then so be it. Each uni will, aside from your own contract, have a large stack of rules of conduct, established routines, sub-organziations and so on and forth; all of that is not influenced by Art 5 whatsoever.
Does this mean, that if I am employed at a German university I can rely on this law, when I do scientific research?
Yes, in so far as the state (legislature, judiciary and executive) cannot restrict you in any way, except for established law or with bringing conflicts with other articles into concordance.
For example, can my professor/supervisor tell me which methods I have to use, which books to read and not to read, how many books to read, etc.? (Of course as long as I stay within legal boundaries)
Yes, completely, at least for your time spent "at work". They cannot tell you what to do or not to do in your spare time.
So, in short, does this law reach into the daily work of scientists or is it just meant to set the boundaries of scientific funding?
All of it, and presumably for some sciences (medicine...) all of the time. Its paragraph 3 protects the whole area of art, science and teaching from the state. The state cannot go in and make it illegal to do science on some specific topic (with exceptions: e.g. embryonic research, animal research, research on humans and probably plenty of others). Paragraph 1 makes sure that the state cannot forbid you or your uni from communicating opinions ("Meinungsäußerungsfreiheit" - literally, "freedom to voice opinion") and to a lesser extent facts (with exceptions: e.g. personal facts covered by GDPR, state secrets, confidential information of your employer etc.).
Finally, if you're reading German, the Wikipedia page on Article 5 GG is a nice commentary and explanation, and as usual has links to sources. Feel free to give it a read if you wish.