The simple and quick answer:
No.
The long answer:
Several things determine compatibility with a processor.
1. The chipset
2. The socket
3. The bios
4. CPU wattage support.
First, all AM3 CPUs are backwards compatible to AM2 and AM2+. So that is no problem.
However, we can now look at the chipset. Since you failed to really give us any information on your computer at all, we cannot find out. AM2 is old though. Most chipsets from that time will not support the newer AM3 CPUs.
Next we have the bios or rather the support of the board. The bios was written to support all CPUs that were out at the time it was made. If you purchase a motherboard and build your own system, the manufacturer of that board may release bios updates as time goes by in order to support newer CPUs. OEM manufacturers (PC system companies like Hp, Acer, Macintosh and Dell) do not release new bios updates for their motherboard because they would rather you purchase a new system than be able to upgrade. Because the bios is not updated and it only supports the older CPUs, behaviour is unpredictable. It may support a newer CPU, but it may run it at a lower clockspeed or do something else strange. Based on that fact that the 1055t and 1090t have 6 cores and new features, it is unlikely they would even work.
Also, motherboards can only support CPUs up to s specific wattage. Based on the CPU support of your computer: "Athlon 64 X2 up to 5000+", I would think the maximum supported wattage would be 65W for you.
The only way to guarantee support is to check the most powerful CPU that your system could be shipped with from the OEM. In your case, as your copy and paste shows, it is the Athlon 64 x2 5000+.
If you would like help or suggestions on alternatives, feel free to ask for them.
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