Well, that's a way of calculating probability distributions (or predicting the chance of certain numbers of outcomes). Just one of many models of doing so, and those results are well, expected (for that distribution model).

But still, per trial, it's a 70% chance. Heck, if you want to rely on the calculator, put in .7 for the probability of success and check the chance for 1 trial/1 success.

Bonus:
According to that calculator, the chance of your outcome of having 15 trials and 5 successes with 70% success rate was 0.3% chance.
That's some luck you got there B|

Every time I see a post like this, it's actually confirmation that the random number generator IS behaving correctly. Why?

Take a player. The probability of that player having a bad streak like yours (or worse) is 0.0037.
Now take 1000 players. The probability that among those 1000 players , there will be someone who has a bad streak like that, is 0.974. Now, who do you think is more likely to complain on the forums? That person who got the bad streak, or everyone else who didn't?

This, incidentally, is why many games actually derandomize* their "random" events. A telltale sign that independent random events are properly implemented is that when your userbase gets large enough, SOMEONE gets screwed over. I'll argue that independent random events are bad game design, but they're definitely not a bug.

*The ideas behind this are actually pretty cool, and there's a decent amount of history behind it. Older RPGs (including the original Final Fantasy, I think) would give you a fixed independent chance (say, 10%) of encountering an enemy every time you took a step. This resulted in streaky behavior (sometimes you would get fight after fight after fight, and other times you would go forever without finding anything), so later games instead randomly set the number of steps you needed to take (say, 5 + a number chosen uniformly at random between 0 and 10) before the next fight, which gave each individual step the same chance (still 10%) of having an enemy encounter, but removing the independence between the steps (so that the more steps you had gone without an enemy encounter, the higher the chance that your next step would be an enemy encounter). Later games with critical hit and dodge chances (such as League of Legends and Path of Exile) use a similar trick: If you haven't interacted with anything in a while, your "critical value" is set to a number chosen uniformly at random between 0 and 99%. When you attack, you add your critical hit "chance" to your critical value; if it breaks 100%, then that hit is a crit (and your critical value rolls over, so 105% -> 5%); otherwise, it isn't. This means that if your critical hit chance is 33%, every third attack of yours will crit, though it's still random in the sense that you don't know whether it will be hits 1-4-7, hits 2-5-8, or hits 3-6-9. (Your critical value gets reset to a new random number if you don't interact with anything for a while so that you can't "store up" a crit by hitting something easy to fight over and over again until you figure out the pattern, and then just before you would crit, stop attacking and go find the thing you really want to fight.) Other times, games will roll a random number each time (like independent events), but after each roll, nudge the success probability by a bit in the direction it takes to balance out the results. For example, if your forge success probability is 30% and you fail, the next time the probability will be 35%, say. This preserves the potential for short streaks (and let's face it, streaks in our favor feel really good) while basically getting rid of long streaks.