$80,000 is above the usual first-time investor's share in an angel fund, and almost as much as the typical non-US startup raises pre-seed (the US has higher valuations than the rest of the world).
People and funds who invest in startups do their due diligence before committing the money. It includes a brief legal check to assess the firm's legitimacy, an economics study done by an investment analyst, a risk assessment, a HR-like look at the founder team and their competences, and expert assessment from people with startup experience.
The complete due diligence process for pre-seed startups costs VC funds about $25,000 (in the US). At this early angel investment stage it still costs a couple thousand. It costs because it takes specialized knowledge to invest in startups.
If you don't have this knowledge, you'll at best be offering what is known as "cheap money" - money given without making sure to get equitable consideration. It's not wrong to do so; some banks are in this business, but they charge interest.
At worst, you or your sister would be essentially gifting the money to the professor, with some hope of maybe making it back. Investment is a business, and here's the business math:
Investing $80k for 5% implies a $1.6 million valuation at no discount, or $2 million at a 20% discount, which the first investor is due. Investors usually expect at least a 10x growth potential for startups, or 3x for low-risk enterprises. So you have to be sure their idea is worth at least $20 million if it's something novel. Even a sure thing like buying items on Alibaba in bulk and retailing them on Amazon would have to be worth $6 million (3x).
People who don't invest professionally, often have very wrong ideas about how it works. For instance, one might think $80k for 5% of a business that will be worth $2M in a year is a 20% win. Not so; businesses fail, so today it's worth much less, and the first investor gets a discount on top of that. If this sounds harsh, that's how VCs survive startup failures and live to invest another day. It took them decades and a few burst bubbles to figure out how to do it.
If the professor is honestly looking for investment, the best course of action is to acquaint them with fair investment practices and accelerators. If you want to invest, you can suggest the idea to any VC fund and see what they think.
If you're new to investing, don't start with this. Leave risky ideas from people without business experience to experienced investors.
P.S. I'm a startup founder, a member of an angel investment fund, and I'm doing postgrad academic research on the economics of startups and startup studios. These synergize. Not quite a drive-by post.