Is it worth upgrading or shall I buy a new system instead?

The first thing you need to think about is how much will it cost for upgrades. Also if this is a laptop, then it may be worth the new computer. If it is a desktop, then you need to see how much the upgrades cost

the problem with upgrading your system is that there are only 2 solutions.

1. stay with amd, means a) wait for ZEn to come out and hope in your budget
2. stay with amd and try a partial upgrade to a faster cpu like an A10 series, which would look like a10-6850K is the very top cpu you can get for it
http://www.gigabyte.com/support-downloads/cpu-support-popup.aspx?pid=4352
would it suffice for your needs, well if your maxing out your cpu right now, perhaps an a10 is all you need. perhaps not. hard to judge

runs you about 100-250$ alone for A10 upgrade
https://www.amazon.com/AMD-Desktops-A10-6800K-AD680KWOA44HL-Thermal/dp/B017WZ1KIQ/ref=pd_lpo_147_tr_t_3?_encoding=UTF8&psc=1&refRID=S2NJ2GQ8BCXS77DMRX34
or
https://www.amazon.com/AMD-Desktops-A10-6800K-Radeon-AD680KWOHLBOX/dp/B00CPLGGXM

3. make over to Intel cpu/mobo and ram, which may seem easy enough throw some cash out and upgrade, but in reality depending on Operating system you have, this may force a full reinstall/reimage of your system, thus saving all your specialized applications, documents etc. form office would be in fact step one. then upgrade hardware and then start over with software. in this case what Is your likely acceptable budget?

lets consider the AMD A10-6800K Passmark of 4,895
against then A6-5400K Passmark of 2133
showing a clear upgrade for 100$ and not much for a headache.

for a lot more you can bring this computer into the 21th century
so we need to compare apple with apple in power of cpu utilization
so we shall compare 4895 score of the A10-6800k as a reference.

and I present the Intel Core i7-6700 @ 4.00GHz with a score of 11,108
so 3 times faster then the core that I suggested that was twice as fast as the one your running, so your looking at a massive improvement in power. or perhaps because of budget I could suggest an Intel Core i5-6600 @ 3.30GHz with a score almost double of the A10-6800K hitting passsmark 7,785 score.

lets talk cost

the first suggestion is CPU with Motherboard that permits to use your DDR3 memory to save cost this isn't a gaming machine, so DDR3 or DDR4 will not make much of a difference.

first with I7 6700.
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i7-6700 3.4GHz Quad-Core Processor ($299.99 @ SuperBiiz)
Motherboard: Asus B150M-A D3 Micro ATX LGA1151 Motherboard ($79.88 @ OutletPC)
Memory: Kingston HyperX Fury Black 8GB (2 x 4GB) DDR3-1600 Memory (Purchased For $0.00)
Memory: Kingston HyperX Fury Black 8GB (2 x 4GB) DDR3-1333 Memory (Purchased For $0.00)
Total: $379.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-01-30 08:06 EST-0500

then with I5-6600
PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-6600 3.3GHz Quad-Core Processor ($213.99 @ SuperBiiz)
Motherboard: Asus B150M-A D3 Micro ATX LGA1151 Motherboard ($79.88 @ OutletPC)
Memory: Kingston HyperX Fury Black 8GB (2 x 4GB) DDR3-1600 Memory (Purchased For $0.00)
Memory: Kingston HyperX Fury Black 8GB (2 x 4GB) DDR3-1333 Memory (Purchased For $0.00)
Total: $293.87

or go all out. with a 6600 CPU and DDR4

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i7-6700 3.4GHz Quad-Core Processor ($299.99 @ SuperBiiz)
Motherboard: Asus H110M-E/M.2 Micro ATX LGA1151 Motherboard ($45.98 @ Newegg)
Memory: Patriot Viper 4 16GB (2 x 8GB) DDR4-2800 Memory ($92.89 @ OutletPC)
Total: $438.86
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-01-30 08:09 EST-0500

You can upgrade the CPU for a better one, the FM2 socket has quad cores available at higher frequencies so that will be a big improvement for sure over the A6 which is a dual core CPU. You should consider upgrading to an A8 or A10 APU. Even now you can already enjoy better performance as the built-in GPU from the A6 performs better than the GT 210.

You could also consider an AMD x4 860/870/880K CPU, and get a dedicated GPU for even better performance. A cheap entry level GPU such as an AMD RX 460 or gtx 1050 is already a much better performer than a gt 210 or any built-in GPU.

You are also mixing different types of ram, which limits the speed of some of them. While you state that your ram runs on different speeds, they actually all run on 1333 mhz. You could get rid of the slow ram and run only the 1600 mhz ram.

https://browser.primatelabs.com/processor-benchmarks
You can compare the current benchmarks listed by running this on your own computer

I searched for compatible CPU for your board and I was stuck right at the start, seems there are numerous versions of this board, do you know which version it is ? if so then you can look at this web page and click the version of your board and see all the possible CPUs compatible with it
http://www.cpu-upgrade.com/cgi-bin/SearchMB.pl?MB=F2A75M-D3H+&ACTION=Search

It seems I have made a mistake in my suggestions. Your motherboard does not support socket FM2+ CPU's, only FM2. This would limit your options to the Athlons X4 740/750/760K. There is a revision 3.0 of your motherboard which is a socket FM2+ motherboard, but seeing your BIOS version I guess your motherboard is one of the 1.X revisions.
These x4 CPU's are not different from the x4 8xx series, so they would be good as well.