Even though this thread is now marked as solved, I'm going to disagree with the prevailing attitude of "if it ain't broke, don't fix it." Basically, you don't know if it "ain't broke." Back in the day, we used to joke about "if it EOJs, it's OK" as a testing methodology. Basically, you can't assume that just because there's no smoke coming from the computer, everything's fine. Your kernel (3.13.0-37) was released something like two years ago (AFAIK -- it's hard to find that information). As you note, that's not even in the same series of kernels as the recommended level of 3.19.0-32. To figure out if there's something broken that you can't see, that might have been fixed between those releases (39 releases in the 3.13 series, 37 in the 3.16 series, and then 11 to the recommended level in the 3.19 series (though I doubt they could be summed up by mere addition)) you'd have to look through all those changelogs to see. The big killer might be any security fixes (things you'd probably almost never see so wouldn't know they were actually broken).
So, my advice would be to 1) back up your data, 2) back up your system (a couple of ways), 3) make sure you've got a usable boot/install disk, 4) gird your loins, bite the bullet, try the latest kernel you can find in Update Manager, and if it doesn't work, back it out. Keep moving back to earlier kernels until you find one that works. If it does work, then you can assume you've fixed as many of those hidden problems as is reasonable. If you don't feel comfortable going to the latest kernel available, at least go to the latest in the 3.19 series (EDIT: maybe not, see Pjotr's comments about the end-of-life of the 3.19 series, below).
As long as you're backed up and ready to recover through various methods, you should be fine (note that I updated my 17.3 Cinnamon all the way to the newest kernel available just after I installed and had no issues -- I usually pop it up to the newest every month).
Last edited by eatenimpinia
on Mon Aug 15, 2016 10:48 am, edited 1 time in total.
Distro: (back to) Linux Mint 17.3 Rosa, Kernel: 4.4.0-51-generic x86_64 (64 bit), Desktop: Cinnamon 2.8.8