So for context I am about to finish my first campaign as a DM for my friend group and we are abut to finish Lost mine of Phandelver and at the end for my custom dungeon I want to transfer them to another world which is the next campaign which is Dragonlance: Shadow of the Dragon Queen. But I do not know what to do with the leveling Dragonlance Shadow of the Dragon Queen is a 1st to 11th level players but my players will start out at level 4 and 5.
So I am wondering should I not worry about the there levels and let them start out as level 4 and 5 or should I fix the leveling for when they start the next campaign so I don't mess something up some help from professional and experienced DM's would help a lot. 

Well, the easiest answer is to either not worry about levels and let the players steamroll the early content as part of "getting used to the new world"" scenario. Slightly less work would be just working an adventure hook that on-ramps your players into the adventure at the 4th-level content and frontloads any information they need from earlier parts of the adventure somehow. And the most work would be altering things so that encounters in the early part of the book are more in line with their current level and jus let them know upfront that it will be a bit before they level again.

I would look at simply increasing monsters #s, HP, and/or AC as a first step toward scaling encounters.  If some fights still seem too easy, you might look at dropping in an extra higher-level creature to some encounters to make them a bit more challenging.  https://koboldplus.club/ can help.  

This link might help as well; https://www.tumblr.com/dmsden/190806964585/taking-the-measure-scaling-pre-made-encounters 

And there are guides in the DMG that can assist in scaling encounters.

It should be doable without too much difficulty.

Maybe you could say that as they were sucked through the vortex, some of their experience/power/magic was sucked from them, and they are starting again at lvl 1. Maybe even you could change the big boss to have 3-4 levels in a class for each of the characters, as if the levels they lost were sucked into the boss. 

P.S. I am kind of new but lots of people say that I am really good at DMing so probably don't prioritize my advice. Besides, in my opinion the players would probably be annoyed to lose their levels, so only do this if you have a kind and understanding party.

Thank you for the people who Replied to my thread I appreciate your input even if you think your own input is bad. 

You could also just kind of narrate through the first few adventures, pausing at key conflicts to ask the players to describe how their character succeeded.

My group calls this a "montage" and we sometimes use it to skip through the first couple levels of a campaign. When starting out, it gives the players a chance to introduce their characters and do some roleplaying. For you the main benefit would be that you all go through the early part of the story together and then drop back into normal play around the level 4 mark. It would be the "steamroll" method, but take 20 minutes instead of 7-8 sessions

I do want to say that monsters are more than just HP and AC. Higher CR monsters are more impressive. After finishing off the BBEG from your last campaign, killing goblins is going to feel kind of like a waste of time regardless of their HP.