Please note that you've posted your question in the SupportAssist for PCs board of this forum, and this Dell utility requires Win 10 or higher. There is a separate board for Dell Latitude laptops at https://www.dell.com/community/Latitude/bd-p/Latitude where you might want to re-post your question if a Forum Moderator doesn't move your thread there for you.
What was your previous operating system (e.g., 32-bit Vista Home Premium SP2), and what is the make/model of your wireless/WiFi adapter? The image below was captured from the Device Manager on my old (now rarely used) HP dv6835ca Vista SP2 machine and shows that this machine has a Intel Wireless WiFi Link 4965AGN adapter that is separate from my Realtek RTL8101E Ethernet (network) card.
Before upgrading, did you run the Windows 7 Upgrade Advisor to ensure your Latitude E5510 hardware and peripherals are compatible with Win 7?
After installing Windows 7 did you activate your Windows 7 license, install Service Pack 1 and patch to end of support (see AdvancedSetup's How to Update Windows 7 to the Latest Security Updates for instructions for patching a clean reinstall of Win 7 back to end of support on 14-Jan-2020)? The free upgrade offer from Vista to Win 7 expired on 31-Jan-2010 and there is no free upgrade path from Vista SP2 to Win 7 SP1 (the usual upgrade path) or any higher Windows OS so most Win XP or Vista users would need to purchase a new Win 7 upgrade DVD and license from a reputable online source (see the Microsoft support article Windows 7 Upgrade Paths for allowable upgrade paths for Vista) to complete the upgrade. Spending that amount of money these days may not be practical given that Win 7 SP1 is no longer supported by Microsoft.
Enter your unique Service Tag <here> on the Overview tab of your Latitude E5510 support page, choose the Drivers & Downloads tab (https://www.dell.com/support/home/en-us/product-support/product/latitude-e5510/drivers), and select your current OS (e.g., 32-bit Windows 7). Do you see a blue "Check for Updates" button (I'm not sure if an automatic scan for updates is available from Drivers & Downloads page for the Latitude E5510). If the "Check for Update" button isn't available choose "This Device" as shown below to find the latest Win 7 compatible BIOS, Intel Chipset driver, wireless/WiFi driver and graphics driver that matches your hardware components. It looks like Dell has not released any Win 7 compatible software or drivers for the Latitude E5510 since May 2016 but your Win 7 OS might still require several firmware and driver updates.