Combine egg whites, sugar, water, almond extract, and corn syrup in bowl of standing mixer or large heatproof bowl and set over medium saucepan filled with 1 inch of barely simmering water (do not let bottom of bowl touch water).
Cook, stirring constantly, until sugar is dissolved and mixture registers 160 degrees on instant-read thermometer, 5 to 10 minutes.
Remove bowl from heat and transfer mixture to standing mixer fitted with whisk attachment.
Beat on medium speed until soft peaks form, about 5 minutes.
Increase speed to medium-high and continue to beat until mixture has cooled to room temperature and stiff peaks form, 5 minutes longer.
Remove bowl from mixer and use rubber spatula to gently fold in almonds.