Linux Mastering Development

Can I run 64 bit ubuntu on my pc (>10 years old)

I don’t know anything about CPUs. I have a 32-bit version of ubuntu. But I need to install 64-bit applications. I came to know that it is not possible to run 64-bit apps on 32 bit OS. So I decided to upgrade my os. But a friend of mine told me to check CPU specifications before the new upgrade. I run this command as was suggested on a website.
lscpu command gives the following details

Architecture:        i686
CPU op-mode(s):      32-bit, 64-bit
Byte Order:          Little Endian
CPU(s):              2
On-line CPU(s) list: 0,1
Thread(s) per core:  1
Core(s) per socket:  2
Socket(s):           1
Vendor ID:           GenuineIntel
CPU family:          6
Model:               23
Model name:          Pentium(R) Dual-Core  CPU      E5300  @ 2.60GHz
Stepping:            10
CPU MHz:             1315.182
CPU max MHz:         2603.0000
CPU min MHz:         1203.0000
BogoMIPS:            5187.07
Virtualization:      VT-x
L1d cache:           32K
L1i cache:           32K
L2 cache:            2048K
Flags:               fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss ht tm pbe nx lm constant_tsc arch_perfmon pebs bts cpuid aperfmperf pni dtes64 monitor ds_cpl vmx est tm2 ssse3 cx16 xtpr pdcm xsave lahf_lm pti tpr_shadow vnmi flexpriority dtherm

In one word what does this mean? I want to know whether I can install 64-bit Ubuntu in my pc.
My installed RAM is 2GB. Since my system is more than 10 years old I expect some expert advice on my CPU status. Should I buy a new pc? Or can I stick with my old one?
I already checked this. But I expect some thing easier.

(I can share any information regarding my hardware, only tell me how to collect them).
Thanks in advance. Sorry for bad english

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