Republican presidential candidate Donald Trump poses for a picture with supporters at the end of a press conference with members of the New York Veteran Police Association in Staten Island, New York.
Republican presidential candidate Donald Trump poses for a picture with supporters at the end of a press conference with members of the New York Veteran Police Association in Staten Island, New York.

Republican Donald Trump and Democrat Hillary Clinton, edging closer to winning their parties' U.S. presidential nominations after decisive wins in New York's nominating contests, are now looking to new elections in five states next week to extend their lead over their remaining challengers.

The next key date in the months-long U.S. presidential campaign is April 26, with Republican and Democratic primaries in four northeastern states -- Pennsylvania, Maryland, Connecticut and Rhode Island -- where pre-election surveys show Trump and Clinton with significant leads. The small state of Delaware also votes next week, but polling has not been conducted there.

Neither Trump nor Clinton has clinched their parties' presidential nominations yet, but both could before Republicans and Democrats hold national nominating conventions in July.

WATCH: Excerpt from candidates' victory speeches

'Mathematically eliminated'

After winning almost all of New York's Republican convention delegates in Tuesday's primary, Trump declared that his chief rival, Texas Senator Ted Cruz, "is just about mathematically eliminated" from winning the nomination before the national convention in mid-July.

Cruz, a conservative firebrand in the halls of Congress in Washington, did not win any convention delegates in the New York voting, but is trying to keep Trump from winning a majority of the convention delegates on the first ballot in hopes of winning the nomination on the second or succeeding ballots.

Republican presidential candidate, Sen. Ted Cruz,
Republican presidential candidate, Sen. Ted Cruz, R-Texas, speaks during a campaign stop, April 19, 2016, in Philadelphia.

Delegate tally

As it stands now, Trump has 845 convention delegates of the 1,237 majority figure he needs to claim the nomination, with Cruz at 559 and Ohio Governor John Kasich at 147. But most of Trump's pledged delegates are only required to vote for him on the first ballot, giving Cruz and Kasich hope that convention delegates could switch their allegiance to them on subsequent ballots.

Trump, a one-time television reality show host who has never held elective office, needs to claim about 53 percent of the remaining delegates yet to be chosen in the 15 states where elections are scheduled through early June to clinch the nomination ahead of the quadrennial national convention, while Cruz would have to win 92 percent of the unclaimed delegates.

Clinton's path to the Democratic nomination in late July is looking close to a certainty, which would make her the first major party female presidential nominee in U.S. history. She would become the first female U.S. president if she wins the November national election to succeed President Barack Obama when he leaves office next January.

FILE - Democratic presidential candidate former Se
Democratic presidential candidate former Secretary of State Hillary Clinton greets supporters during a primary election night gathering on April 19, 2016 in New York City

'Home stretch'

After winning in New York, Clinton told supporters, "The race for the Democratic nomination is in the home stretch and victory is in sight."

Clinton, the top U.S. diplomat from 2009 to 2013 and the wife of former President Bill Clinton, needs 2,383 Democratic convention delegates to win the party's nomination. After her New York victory, she has 1,930 delegates, far ahead of her sole challenger, Vermont Senator Bernie Sanders, with 1,189.

She made a plea to Sanders's voters to join forces with her, telling them, "I believe there is much more that unites us than divides us."

Clinton needs only to win about 28 percent of the 1,646 convention delegates yet to be chosen to become the Democrats' standard bearer in the November election.

New Yorker Pamela Hamilton attended tonight's Hill
New Yorker Pamela Hamilton attended Hillary Clinton primary night party and voted for her earlier in the NY primary, April 20, 2016. (T. Trinh/VOA)

Convincing victories

Trump and Clinton won convincing victories in their home state. Trump has developed numerous projects in New York and lives there in a luxury high-rise building, while Clinton has made New York her adoptive home and was twice elected to the Senate from the state.

Trump got about 60 percent of the vote in the Republican primary, with Kasich at 25 percent and Cruz at 15 percent. Clinton beat Sanders, 58 percent to 42 percent.