An arithmetic progression has a common difference of -2 bpm. If the heart rate at the 24th hour is 68 bpm, what is the heart rate at the 19th hour?

The heart rate at the 24th hour is 68 beats per minute (bpm). We can denote this as $a_{24} = 68$.
The heart rate is decreasing by 2 bpm each hour. This means the common difference $d = -2$ bpm.
We need to find the heart rate 5 hours before the 24th hour, which is at hour $24 - 5 = 19$. So, we need to find $a_{19}$.

The formula for the $n$-th term of an arithmetic progression, given a $k$-th term, is:

We want to find $a_{19}$, and we know $a_{24}$. So, let $n=19$ and $k=24$.

The heart rate at the 19th hour is $\boxed{\text{78 bpm}}$.