Let's take a look at your system specs:
CPU
- Intel Core i5 (3rd Gen) 3230M / 2.6 GHz
- Max Turbo Speed 3.2 GHz
- Number of Cores: Dual-Core
- Cache: 3 MB
- 64-bit Computing: Yes
- Chipset Type: Mobile Intel HM77 Express
- Features: Intel Turbo Boost Technology 2.0
RAM
- Technology: DDR3 SDRAM
- Installed Size: 4 GB
- Max Supported Size: 8 GB
- Form Factor: SO-DIMM 204-pin
- Slots: Qty 2
Hard Drive
- Type: HDD
- Capacity: 500 GB
Your system specs meet the minimum requirement for Ubuntu 16.04 as stated in your question.
Steps to modernize and improve speed
If you use Google Chrome or Firefox the best step you can take is to increase your RAM from 4 GB to 8 GB. A local computer retailer can quickly help you out with that. An additional 4 GB of RAM should cost you about $30 plus installation.
The biggest speed improvement will be upgrading your 500 GB HDD to an SSD. You can take your old HDD, put it in a $25 USB enclosure and use it for backups / slow storage. A 256 GB SSD will cost you $50 to $150 depending on sales and name branding (ie Samsung Evo 850 is name brand).