https://www.moe.gov.sg/-/media/files...u-ges-2020.pdf
Realistically speaking, your seniors in
NTU other than CS and Double Degrees, none of the other Engineering degrees hit 5k in the 75th percentile for their starting salary.
For private sectors, unless you do exceptionally well for the technical assessments its hard to justify for your starting salary since your peers across engineering degrees are willing to accept it lesser.
But like the other commenters suggested, public sector and academia looks heavily on your education cert so they are likely to offer you higher than 5k. Actually banks also look at your cert, so you could likely get offered more than 5k in tech for FCH.
There are also high paying startups in tech like quant and forex stuffs. If you do well its likely you can also hit 10k monthly salary in a short 1-2 years. I have a peer who went into this field. Sounds nice but heard that its much more stressful than SWE.
Also the 13th month package and bonuses. Not every company gives it. So the annual package for a $5k salary without bonuses and 13th month is $60,000, is lower or equal to one with bonuses and 13th month with a base salary of $4615.39 (60000/13).
The above is just purely about salary. I have many friends who were paid 20+ to 50+% higher starting salary than me (normal cauz they are HD/D compared to me almost no merit) finds trouble job-hopping few years later because their work is very niche in the market, no excellent portfolio, already lost touch in technical tests. Many of them developed low self-esteem from couldn’t even secure an interview and poor career progression in their current work. A few of them even start to show signs of becoming some grumpy uncles and aunties who just find fault about everything and everyone for their circumstances except themselves. The competition doesn’t stop after your FCH, it only ends after you retire.
Genuinely hoping you will find happiness rather than fixated on winning your peers. I’m sure you are worth more than the 5k starting salary. Aim towards gaining all the specialised skillset and the numbers will soon follow, maybe many times higher than 5k. Good luck.