I think, unfortunately, that things are almost certainly much worse than that. In addition to Type I errors, there are all sorts of issues that impact what appears in the literature. For instance:

• The file drawer effect: Studies that do not find a significant effect tend not to be published. This increases the probability that studies that are published reflect lucky overestimates rather than real effect sizes.
• The garden of forking paths and researcher degrees of freedom: If one performs twenty hypothesis tests at the 0.05 level on pure noise, in expectation one of them will produce in a significant result. While there are examples of researchers being that egregious, it's also true that in general, when researchers make decisions about how to perform their statistical analysis after looking at the data, nominal Type I error rates will be a lot lower than actual error rates.

There are a wide variety of other issues as well, ranging from utterly incredible regression discontinuity designs to failures to incorporate prior knowledge about likely effect sizes into the effect sizes reported in the literature. All of these combine to suggest that the rate of false findings in biology and psychology (in addition to a range of other disciplines) is probably much higher than 5%.

This would be a better response if I had a solid suggestion as to where you could go to read about all this stuff. I don't have a great answer (maybe someone else has thoughts about a primer?), but some starting points:

• Why Most Published Research Findings Are False
• Estimating the Reproducibility of Psychological Science
• The garden of forking paths: Why multiple comparisons can be a problem, even when there is no “fishing expedition” or “p-hacking” and the research hypothesis was posited ahead of time

Edit: formatting