You have five attempts for each course at JKU. There are exceptions during the introductory and orientation phase (StEOP) at the beginning of your bachelor's or diploma program: here you only have four attempts.
Please also note that for combined programs (e.g., teacher training), the number of attempts may also be reduced to four.
You have one more attempt for your final exam in your degree program.

All exam attempts for the same exam subject in all degree programs at the same university count towards the calculation.
Exams differ depending on the type of course: for a lecture, each exam date attended counts as an attempt; for exercises, there is only one continuous attempt per semester, which consists of exercise sheets, tests, etc. So, even if several practice tests are offered for exercises, it is still only one joint attempt. Courses are usually treated like exercises.
You receive a grade in KUSSS for each attempt.

If you did not do anything for a subject, it cannot be counted as an attempt. So, for example, if you do not show up for a lecture exam, you cannot be graded.

From the third repetition of a lecture exam onwards, it must be held “before a commission” – more on this below!

Even a positive grade can be repeated if you hope to achieve a better one: The repetition can take place once and only within one year.
Please note: The old grade will be invalidated.
§ 35 ST-StR

In an exam by commission, it is no longer a single person who decides on the grade, but an examination board (§ 32 ST-StR). It is therefore a mechanism designed to ensure that you are not treated unfairly.

In lecture exams, your submission is checked by several people, while in exercises and similar activities, an attempt is made to concentrate your continuous performance into a single moment and check it in an exam by commission.

From the third repeat of a lecture exam onwards, it is mandatory to hold an examination by commission, but you can also apply for one for the second repeat (§ 77 (3) UG). Regardless of the type of course, at least the last attempt must be held as an exam by commission (§ 35 (3) ST-StR).

Teachers are obliged to give you a grade no later than four weeks after your last assessment (e.g., exam or last exercise session). § 34 (2) ST-StR

Within six months, you may request access to the assessment documents - in the case of exams, this is the corrected written exam, and in the case of an oral exam, a transcript of the questions you were asked.
You may photograph or otherwise reproduce open-ended questions and your answers; multiple-choice questions are excluded from this. § 79 (5) UG

The same right of access also applies to assessment documents relating to your thesis. § 84 (2) UG

No legal recourse is available against a grade - in particular, it is never possible to “improve” the grade.

Only negative grades can be contested, and only if there is a “serious deficiency”: These include insufficient exam time, questions that are unrelated to the exam material, or an exam before a commission in which not all committee members are present (Kommentar). If your appeal is successful, the grade will be revoked, but the hurdle for such a revocation is very high.
If the grade is revoked, your negative grade will be deleted, meaning you will “win” your attempt back. This option is particularly interesting if you have already attempted the exam several times.

The request for annulment must be submitted within four weeks of the assessment. § 79 (1) UG

In addition to annulment due to serious deficiencies, positive grades can also be declared invalid if the exam does not meet the standard of an exam. E.g. completely inventing grades would fall under this category, as would grading students who did not even take the exam. Kommentar

If you are afraid of being treated unfairly, you can either request an examination by commission or submit a request to choose your examiner. 

From your third attempt in a subject onwards, your request must be granted, provided that the person you have chosen is also qualified to conduct the examination.
Before that, your request will only be considered “if possible.” § 59 (1) Z 13 UG

In practice, this usually means that you will be examined by another person from the same institute, but theoretically, the examiner may also be from another university. In the case of joint degree programs such as teaching or biological chemistry, this option is explicitly provided for by law, and can thus offer you very effective legal protection against unfair assessment.

Oral examinations are public, i.e. accessible to everyone – even when held digitally. However, the permitted number of spectators may be adjusted to the size of the room.
You must receive the results of your exam immediately after the exam, and if you receive a negative assessment, the reasons must be explained to you. § 79 (2) UG

Upon request, you must also be given the reasons in writing. § 79 (4) UG

Cheating is – unsurprisingly – not permitted and is punished severely at JKU. This includes plagiarism or fabricating data, but also the use of unauthorized aids, etc: You can even be punished if the aid was only kept ready for use.

Your assessment may be declared invalid, and in serious cases, you may even be “forced to take a leave of absence” for up to two semesters, meaning you will not be allowed to take any more exams. § 38 ST-StR