Just picked up this feat and have no idea how to have it automatically subtract 5 from my to hit rolls and add 10 to my damage.  This is on Roll 20 VTT using D&D Beyond and the Beyond 20 extension to Chrome.

Sadly the only thing you can do at this time is the math in your head.

If you are using the Beyond20 app to integrate your rolls from DDB to Roll20, you can set a hot key option that will do sharpshooter. 

Simple, add another weapon to your inventory, rename it with (Sharpshooter) and modify the to hit and damage rolls appropriately.

When you use the feat, click that weapon for the rolls.

You can also create a wondrous item, that when equipped gives you the modifieres. This would be compatible with every magical weapon you may have.

Unequip after use and you are good.

Looks like this:

Quote from MarquisAndras >>

Simple, add another weapon to your inventory, rename it with (Sharpshooter) and modify the to hit and damage rolls appropriately.

When you use the feat, click that weapon for the rolls.

Quote from Voras >>

You can also create a wondrous item, that when equipped gives you the modifieres. This would be compatible with every magical weapon you may have.

Unequip after use and you are good.

Looks like this:

Wondrous Item, common

 

-5 to Hit / +10 DMG while equipped.

Notes: Bonus: Melee Weapon Attacks, Damage: Melee Weapon Attacks

 Both of these options will work. Disregard Wheeliekid.

Thank you all.  The wondrous item looks like the best way to go.

I prefer Marquis’s suggestion. To add to their suggestion, change the weight of the new weapon to zero so you don’t overencumber yourself. 

I built a character with Sharpshooter and had my Longbow and SS Longbow which both showed in the “attack” section and I just clicked on the one I wanted to roll with Beyond20 on Roll20 from my DDB character sheet. And I didn’t have to equip/unequip an item each time. 

Quote from Voras >>

You can also create a wondrous item, that when equipped gives you the modifieres. This would be compatible with every magical weapon you may have.

Unequip after use and you are good.

Looks like this:

Wondrous Item, common

 

-5 to Hit / +10 DMG while equipped.

Notes: Bonus: Melee Weapon Attacks, Damage: Melee Weapon Attacks

To be clear, the modifiers listed here would apply if you were doing this for Great Weapon Master. If you wanted to do it for Sharpshooter, you would want to pick the Ranged Weapon Attacks.

This is the worst option to solve this issue though. SS & GWM are a called shot type of effect, I wouldn't even consider them a temporary effect. The issue with using a wonderous item to apply to all melee attacks or all ranged attacks is what are you going to do when you don't want to call your shot before hand. You have to go unequip our SS/GWM wonderous item to get your numbers back to normal. Try and remember to do that after you've spent 3 weeks trying to put together a session, gone through an hour or role playing and exploring, 3 rounds of combat where you're 7th out of 12 combatants, and for whatever reason you forget to turn it off for this round. This is more of an issue with GWM since it only applies heavy weapons and PCs might have heavy and non heavy weapons, whereas SS applies to all ranged. 

MarquisAndras had the easiest solution of adding a 2nd copy of your weapon and customizing it to apply the adjusted modifiers. Since you're using the Beyond20 extension, Lathius suggestion also works. These two solutions don't work together though.

Yeah I definitely think of the suggestions provided, duplicate weapon you can just click to attack with > wondrous item that you need to remember to turn on/off.

Depends of course on your character or character sheet.

I play a Warforged Rune Knight with GWM and it carries a regular Dagger, a +1 Dagger, 2 Handaxes, 4 Javelins, a Maul, a silvered Greataxe, an Adamentine Greatword, and a Warhammer.

I do not want to add 3 more lines with GWM attacks to my sheet, ending up at potentially 11 rows of possible close combat attacks (+ unarmed strike), so the wondrous item is much more convenient in my opinion.

Both options are totally viable.

Quote from Voras >>

Depends of course on your character or character sheet.

I play a Warforged Rune Knight with GWM and it carries a regular Dagger, a +1 Dagger, 2 Handaxes, 4 Javelins, a Maul, a silvered Greataxe, an Adamentine Greatword, and a Warhammer.

I do not want to add 3 more lines with GWM attacks to my sheet, ending up at potentially 11 rows of possible close combat attacks (+ unarmed strike), so the wondrous item is much more convenient in my opinion.

Both options are totally viable.

As long as you're aware the modified To Hit and Damage rolls do not apply to the daggers, handaxes, javalins, and Warhammer, I guess you're ok.