if I have a 3% chance to summon a magic spear every 1 strokes, what is the percentage chance that I will invoke the spear every 5 strokes?
Attemp: I don't think this is correct; if I'm not mistaken, the question is asking the probability that only one spear is invoked every 5 strokes. Then, the probability would be $\binom{5}{1} \cdot \frac{3}{100} \cdot (\frac{97}{100})^4 = 0.13279...$ so the answer is about $\boxed{\text{13.3 percent}}$.
Much of the work of a probability problem like this is translating the question into terms that are more "probabilistic".
If each stroke has a $3\%$ chance to summon a spear, you can treat the summoning of a spear in one stroke as a Bernoulli variable with $p=0.03$, that is, probability $0.03$ of success.
If you have a sequence of $5$ strokes, and each has an independent chance to summon a spear, the number of spears summoned is a binomial variable $X$ with $n=5,$ $p=0.03$.
You appear to have correctly intuited this, because the formula $\binom{5}{1} \cdot \frac{3}{100} \cdot (\frac{97}{100})^4 \approx 0.13279$ is the correct formula for the probability that $X=1$ (you summon exactly one spear) if $X$ is defined as above.
To summon at least one spear, notice that the only way you will not summon at least one spear is if you summon no spears at all. So compute the probability that $X=0$ (no spears). Then when you subtract that probability from $1,$ what is left will be the probability that $X \neq 0,$ which is the probability that you get at least one spear.
As you probably know, $P(X=0) = (\frac{97}{100})^5$ in this example.