Hi Zed,
Managing an independent connection is a really important topic that needs careful analysis to make the right choice.
Also consider whether you're traveling with one or more checked bags. In that case, add the baggage delivery time (I waited a good half hour for mine recently in Barcelona).
There are 3 possible scenarios with their pros and cons:
1°/ :
Your example with about 5 hours between the two flights.
Plan to be at check-in at least 2 hours before departure, so around 9:30 PM for the Singapore flight. If the first flight is on time or has a 2-hour delay, you theoretically have time to collect your checked baggage (assuming you check one), go through immigration (e-gate in Singapore, and make sure to fill out a second SG card), and possibly change terminals.
Map

So yes, on paper, it’s doable, and you have roughly a 2-hour buffer.
Any delay longer than about 2 hours, though, and you start running into issues (I’ll come back to this). The same goes if your flight is canceled (on the day or before), as the airline will have to offer an alternative based on availability. If the replacement flight doesn’t allow you to make your connection, you’ll have to handle everything yourself—it’ll be your problem, not theirs.
What if a delay or cancellation means you can’t make your connection?
Deal with the airline in Singapore by asking for a date change. First, hope your ticket is changeable (often with a penalty—check the terms). Keep in mind there might also be a fare adjustment depending on availability (very common and can be expensive), not to mention limited seats on later flights (risky in peak season) and your own schedule.
If you can’t reach the airline for any reason, you’ll be marked as a "no-show," risking losing your ticket. At best, you’ll face the changes mentioned above.
In the end, this scenario can get expensive if your flight is canceled last minute or significantly delayed. It’s a gamble on the reliability and punctuality of a specific flight. You’ve got to be okay with taking that risk and potentially losing out.
2°/:
You leave the same day but earlier—maybe even in the morning. This way, you limit risks in case of delays, and if there’s a cancellation, you have more time to sort things out. You also have the option, if absolutely necessary, to buy a new ticket (at what price?) on another airline to catch your connection.
If everything goes smoothly, you’ll spend extra time at the airport. Otherwise, check if there are lockers and go for a walk.
3°/ :
You take your Bali/Singapore flight the day before. This eliminates all delay risks, gives you time to handle cancellations, removes stress, and lets you control your budget with just one night’s stay. Plus, you’ll be less tired by splitting up the trip.
To sum up, with an independent connection, you’re either okay with taking risks and dealing with potential issues and financial losses, or you’re not, and you leave the day before.
Also consider the airline. Low-cost carriers might not have a desk at the airport, so everything is handled via their website, phone, or messaging. Not always easy, especially abroad.