2 modes of radioactive decay for hydrogen-5? While looking at a table of helium isotopes it said that helium-8 turns into Tritium(hydrogen-3) and helium-5 through fission and beta decay.

But the pathway to helium-5 isn't so direct. It is more like this

helium-8 -> hydrogen-3 and hydrogen-5 (fission) -> helium-5 (beta decay)

But the table of hydrogen isotopes said nothing about hydrogen-5 going through beta decay. All it had there was double neutron emission producing tritium which after 12 years turns into helium-3 via beta decay.

Does this mean that I discovered that hydrogen-5 does go through beta decay but not nearly as often as double neutron emission?
Sorry, you haven't.  I don't know where your information is from but I think there is an error in your decay chain.  For the 0.9% of $\ce{^8_2He}$ decays that proceed via spontaneous fission your equation should look more like this:
$$\ce{^8_2He -&gt;[fission] ~^3_1T + ^5_1He + \beta ^{-}}$$
$$\ce{ ^5_1He  -&gt;[neutron~emission]  n + ^4_2He} $$