I agree with what has been posted. You probably don't need a different line. IMO, until you get into heavier weights, you won't likely see a lot of difference in what you have & a specialty line, particularly since you're new to this. Improving your casting technique with bigger flies, will likely do the most good. As far as specialty lines go, all line weights, the first 30 ft or so will weigh about the same with the same sizes. The difference is in how the tapers are designed. A specialty line, like a Bass or Tarpon, or Striper line, with a much shorter front section will place the heaviest part of the taper closer to the leader, which is desired for casting bigger flies, more wind resistant flies & in windy conditions.
Frankly, I have a couple of different specialty lines, & can't see much difference in them, because much of the fishing I do is within 35-40 ft of myself. Get out in distance & yes, they help, but otherwise they all cast pretty much the same. I've cut that front section shorter too on some lines, that basically made them like the specialty lines, and I didn't need to buy another line. It all depends on what you need the line to do. My bass lines are the same ones I use for Striped bass & I often use the same flies. Whether I'm fishing in a small creek or in an open bay, the same lines still fit my fishing. I rarely have the need to roll cast or even mend line, but when I do, I understand that the lines have limitations for doing this.
I've also done a lot of bass fishing with a 6 wt. My rod is actually a 5/6wt but I've never had anything on it but a 6 wt line, and it's always been fine for most bass I've caught. I get a bit more extreme now, & often use a 9 or 10 wt for really big flies & in some really nasty, snag filled places. You don't want to do that with a 5 wt, but for small stream bass, I'll even use a 3 or 4 wt. I'm certainly not going to be casting the same size flies, but don't need to.
I agree with what dpreller posted about fly sizes. I'm an advocate for bigger flies/bigger fish, however, that's not a set in stone attitude. It works some places at some times, but not for all situations. Increasing fly size when it's necessary can be productive, but is no guarantee you'll catch any more fish, or of bigger sizes. Bass will eat many things of various sizes. If what you've been using is producing where you're fishing, then why change it? I also like to have variety available, so I'll carry flies that are bigger & smaller than I might need. You can't use what you don't have available. If you feel that some bigger flies will be useful, then of course add a few, just don't go crazy with the sizes. For a 5 wt, a size 4 streamer, perhaps about 2 1/2" long is probably about as big as you'll want to go. Even a longer fly can be cast with with a 5 wt, but with increased wind resistance will usually limit distance.
Ideally, going to saltwater with a 5 wt is not the best choice. Simply because conditions will most often dictate something with more power to even cast short distances. Wind being the biggest problem. However, use what you have unless you're in a position to add a heavier weight outfit. Just be aware of the limits. You may need to shorten your leader & go stouter with the tippet if you go with heavier or bigger flies, but it can be done. I've cast 2/0 size saltwater flies with my 6 wt, but only short distances & when the situation presented an opportunity & the 6 wt was the only rod I had available at the time.
One more thing. I know many folks who will only fish with a fly rod. I'm not one of them. I enjoy fly fishing the most, but understand it's not always going to be the best tool. If the conditions allow, regardless of what you bring, then use what you have, but don't try to force the issue as that will only lead to frustration. I've been stubborn enough in the past to try & toss flies, when even using a baitcaster would have been nearly impossible. I learned that a fly rod is a tool, to be used when the conditions allow,(particularly in saltwater) and even though I'm still stubborn, I've learned to make better decisions concerning whether or not I'll try to throw flies.
I have no issue with using other gear!
Use the right tool for the conditions if you're intent on fishing!