Basements, Attics and Crawl Spaces - Garage Loft

First time on this forum so not sure if this is the right place/format for this question. I'm building a storage loft in my garage. The length is 19' x 8'. 19 feet is wall to wall and the 8 feet is how far out I want to come. My plan is to lag a 2" by 10" on the 2 ends and either run 2 x 10's every 16 inches using joist brackets or put them on top of the lagged planks but only if it's needed because it will obviously take up more height. (Sorry if this doesn't make sense. I'm fairly handy but sometimes don't know how to word it.

This will be a loft for storage (Christmas decor/boxes of clothes/random stuff - probably not more than 5,000 lbs total). Also, do I need to use 2 x 10's for the joists or can I use 2 x 8's?
Thanks a lot for the help!

Welcome to the forums! You will need to lag your 2x10 to the back wall studs as well as the side wall studs, use the joist hangers and 2x10's for joisting. Now, comes the trick. Your front 2x10 will need supporting as you can't span 19' with a single dimension lumber piece. So plan on having a support post in the middle and doubling the front rim.
5,000 lbs???? Remember your SUV doesn't weigh that much, so consider a realistic weight factor for that area, and adjust accordingly. I am assuming you will access it from the garage side via a ladder of sorts?
You may be able to use 2x8's if you consider your weight factor, since the 2x8 can span 8' clear.