Given your income, expenses and the provided property prices, you don't need to do much to afford a house. Just leaving the money in your bank account while you save should be enough to afford a house in your area within 5 years, even if you had no pay raise.
For the rest, ask your bank, and go to a second one to see what they suggest. I don't think any other place makes sense because they will not provide a better / cheaper offering and you need a bank for your loan anyways. A bank can show you ways to save money in a secure way, explain if a so called Bausparer is beneficial, can help with funding (Kredit) and know details about potential tax benefits and state funded support (cheaper loans etc). Your local bank will also know the local housing market well.
A few things to consider:
- Don't buy stocks, (bond) ETFs, funds: chances are you may actually make a lot of money in 5 years, but it may also drop 30% - 40% just before you would want to buy a house
- Try to get a good interest rate on a term deposit (Spareinlage / Sparbuch in Austria; the latter likely has higher fees, so try to avoid it). 20.000 at 3% for five years will return about 23.185. in total, you will be way above the required 80k at the time of writing if you save 20k per year, for 5 years, and get interest. Realistically, it will be around 110k.
- Alternatively, buy bonds (Anleihen) from companies with a low chance of default. They should pay about 4 percent interest at the time of writing. Make sure they expire at a time you want to start to look for houses on the market(e.g. in 5 years).
With regards to the housing market, the market conditions don't matter too much. It's difficult to predict what will happen. Also, you cannot buy now, and you don't want to wait too long either it seems.
Bottom line, if you just save the current disposable income for 5 years, you should be able to buy a decent house.